Questions on the evaluation of derivatives or problems involving derivatives (for example, use of the mean value theorem).

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1answer
21 views

Derivative of logistic loss function

I am using logistic in classification task. The task equivalents with find $\omega, b$ to minimize loss function: That means we will take derivative of L with respect to $\omega$ and $b$ (assume y ...
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0answers
22 views

Please help me check this derivative work

I have $$ J_{\theta}(X) = - \frac 1 m \cdot \left[ y \cdot ln( h_{\theta} (X ) ) + ( 1 - y) \cdot ln ( 1 - h_{\theta}(X) ) \right] $$ I need $\frac d {d\theta} J_{\theta}(X)$. I tried many time, and ...
2
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2answers
94 views

Derivative of $(-2)^{x+1}$ [on hold]

Can we compute the derivative of $(-2)^{x+1}$? This may sound silly, but think about it. We cannot apply any of our formulae on it. I think we may have to go old school with this one
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1answer
22 views

Sign convention for derivatives in a $\mathbb{Z}_2$ graded space

Suppose $V=V_0\oplus\theta V_1$ is a $\mathbb{Z}_2$ graded super vector space. Note: Since $\theta^2=0$, this implies $\theta\mathrm{d}\theta=-\mathrm{d}\theta\cdot\theta$. However, I wish to know ...
-1
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1answer
40 views

Math question: Calculus [on hold]

"A rancher would like to enclose two adjacent rectangular corrals that cover a total area of $12,000 ft^2$. If material for the fence costs $3.5$ usd per foot, find the dimentions (length and width) ...
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0answers
16 views

How to solve this problem about production and derivatives? [on hold]

If p(x) is equal to the production of a factor when there are x workers, then the average productivity of the work force is: A(x) = p(x)/x a) Find A´(x). Why does the factor need to hire more ...
2
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2answers
37 views

How to find derivative of an integral of this type

$$f(x) = \int _x^{e^x}\:\left(\sin t^2\right)\,dt$$ How to find the derivative $f'(x)$ Attempt: $\sin (e^{x^2}) e^x$
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0answers
11 views

Derivative of a generalized hypergeometric function

Let $$f(a)={_2F_3}\left(\begin{array}c1,\ 1\\\tfrac32,\ 1-a,\ 2+a\end{array}\middle|-\pi^2\right).$$ How to find $f'(0)$ in a closed form?
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1answer
26 views

First derivative of this secial function

What is the derivative of the following function: $$f(x) = \frac{a}{((\sqrt{b+bx})(d-\sqrt{e+gx}))^2}$$
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3answers
52 views

Showing $\lim_{n \to \infty}\left(1 + \frac{x}{n}\right)^n = e^x$ using implicit and log differentiation

Hey guys I'm looking over my review sheet for an upcoming test and I'm having trouble with this problem. Apparently I'm supposed to use implicit differentiation and log differentiation, and I'm ...
0
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2answers
24 views

Find range of values

Find the range of values of the constant $a$ at which the equation $x^3 - 3a^2x + 2 = 0$ has $3$ different real number roots. I took the derivative and found that $x = -a, a$ Then I solved for $f(a) ...
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0answers
29 views

Summation of Recurrence (Convergent series)

I have solved this issue. Would you please verify whether I am correct or not? Motivation for the post is our previous discussion link.I am restating my problem with additional elaborated explanation ...
1
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2answers
37 views

$\dfrac{\partial}{\partial x}\left(\int_{g(x)}^{h(x)}f(y)\, dy \right)= f(h(x))h'(x)-f(g(x))g'(x)$

I'm trying to prove the following, interesting, relation: $\dfrac{d}{dx}\left(\int_{g(x)}^{h(x)}f(y)\, dy \right)= f(h(x))h'(x)-f(g(x))g'(x)$ I tried to integrate by parts the RHS, but i don't ...
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3answers
24 views

maximum area of a rectangle inscribed in a semi - circle with radius r.

A rectangle is inscribed in a semi circle with radius $r$ with one of its sides at the diameter of the semi circle. Find the dimensions of the rectangle so that its area is a maximum. My Try: ...
0
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2answers
48 views

Differentiability at x=0 [on hold]

Discuss the differentiability of the following function in $x$ = $0$: $ f:\mathbb{R} \to \mathbb{R}: x\mapsto \begin{equation} f(x)= \begin{cases} \sqrt{x} & \text{if } x \geq 0 \\-\sqrt{-x} & ...
0
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1answer
17 views

Find the rate of change. $P=250(1+(2t/(49+t^2)))$

A population of bacteria is introduced into a culture. The number of bacteria $P$ can be modeled by $P=250(1+(2t/(49+t^2)))$ where $t$ is time (in hours). Find the rate of change of the population ...
5
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2answers
98 views

Is $\int^x \cos \frac1t$ differentiable at zero?

From Spivak's Calculus, 4th ed., exc 14-20: Let $$f(x) = \begin{cases} \cos \frac1x, & x\neq 0\\ 0, &x=0. \end{cases}$$ Is the function $\int_0^xf$ differentiable at zero? I'm having ...
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0answers
53 views

second order ODE :- solution

We have $y''-Py'-Qy = 0 $ where P,Q are $P = K_1+K_2x, Q =K_2 $. $K_1,K_2$ are constants. y' means derivative with respect to x . Please suggest a solution for y. Thanks
1
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1answer
12 views

Inverse Laplace transform, none factorable denominator

I am really stumpted on this problem and can't seem to figure out where to go from where I am. Can anyone give me some advice or hint where I should do next? Here is the problem: ...
0
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2answers
40 views

The fundamental difference that determines when a derivative can be calculated directly or only using the chain rule

I was given the following problem: Find $\frac{dy}{dx}$ using the implicit equation $x^2 + y^2 = 1$ What I'm more interested in is the explicit equation, $y = \sqrt{1 - x^2}$ (I'm allowed to ...
3
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0answers
36 views

Find all differentialbles function [on hold]

Find all differentialbles function $f:[0,\infty)\rightarrow\mathbb R$ such that: a) $f^{\prime}$ is non-decreasing; b) $x^{2}f^{\prime}(x)=f^{2}(f(x)),~\forall x\in\lbrack0,\infty)$
4
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1answer
78 views

Derivative in 0

I'm a highschool student and we don't learn maths in English. So please excuse me for my Math's English. I'm doing an exercise and I can't answer its final question. Can you help me? Thank you! Let ...
4
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1answer
96 views
+200

Determining the maximum value for the solution of this delay differential equation?

I am working on the following delay differential equation $$\frac{df}{dt}=f-f^3-\alpha f(t-\delta)\tag{1},$$ where $\frac{1}{2}\leq\alpha\leq 1$ and $\delta\geq 1$. I know that there are three ...
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1answer
23 views

Continuity of fixed points of an equation

Say I have a function $f(x,\theta)$ such that for each value of $\theta$ the function $f$ has a unique fixed point $x^*(\theta)$, i.e. $$x^{*}(\theta) = f(x^{*}(\theta),\theta)$$ My question is when ...
0
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1answer
44 views

Find $\frac{dy}{dx}$ of $y=\sqrt{u}$

Find $\dfrac{dy}{dx}$ of $y=\sqrt{u}$, $u=7-x^2$ This is on my homework and I don't know what to do exactly. Steps would be helpful!
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1answer
51 views

Second derivative of this function [closed]

Whats is the second derivative of the following function? $$f(x) = \frac{0.12}{\sqrt{(0.01+0.24x)}\;(1.1-\sqrt{0.01+0.24x)}}$$ I get the first derivative as follow, but I am not sure is it correct ...
0
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1answer
26 views

Derivative from Graph

Hi, I am trying to study a bit ahead for my calculus class next year and I came across this question. I was wondering how to find the derivative of the graph without the function. I figured I could ...
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2answers
21 views

Determine the point(s), (if any), at which the graph of the function has a horizontal tangent.

Determine the point(s), (if any), at which the graph of the function has a horizontal tangent. $y(x)= x^4-500x+2$ So I know the first thing to do is find the derivative which is: $y'(x) = 4x^3-500$ ...
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1answer
34 views

Having derivative in some $x_{0}$ implies having it in $U(x_{0})$ [closed]

Let $f$ be continious function in R and it has a derivative in $x_{0}$. Does it have derivative in some $U(x_{0})$?
3
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2answers
49 views

The right procedure on difficult related rates problems

I'm pretty sure the sample problems my teacher gives to us violate some article of the Geneva convention. I'm in talks with my embassy about that, but in the mean time maybe you guys could look over ...
1
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1answer
36 views

Why does secant method converge

Assume $f$ is continuous and twice differentiable on $[a,b]$ such that $f'(x)>0$ and $f''(x)>0$, $x \in [a,b]$. If $f(b)>0$ and $f(a)<0$ and I choose $x_0=a$,why are we gauraunteed ...
0
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2answers
24 views

Find dx/dt given that x=-8, y=9, and dy/dt=5

I have this question on my homework assignment. Assume that x and y are differentiable functions of t. Find dx/dt given that x=-8, y=9, and dy/dt=5. Equation: y^2-x^2=17. There are examples in the ...
2
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0answers
21 views

Rendering the derivative of composite functions from a graph

I'm on a workbook problem and I want to make sure I'm doing it properly. The problem asks me to find the derivatives of composite functions when given only the graphs of the original functions, here ...
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4answers
66 views

Derivative with respect of a function

i have a function of two variables: $f(\theta,\phi) = \theta \sin(\phi)$ and i have to differentiate $f(\theta,\phi)$ with respect to: $1 - 0.5\theta^2$ That is: ...
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1answer
47 views

Having trouble with differentiating under integral sign

I am sorry if this seems like a dumb question, but I am having trouble in applying differentiation under the integral sign to definite integrals such as this one: $$\int^{1}_{0} ...
0
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1answer
58 views

Partial derivative and derivative.

I want to show that if $f:\mathbb{R}^n\to \mathbb{R}$ and $df_a$ is the derivative of the function at $a$ then $df_a(v)=\displaystyle\frac{\partial f}{\partial v}(a)$. I saw a few proofs of this ...
0
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1answer
41 views

Solving ODE with matrices

I have an equation in ODE $M{'}(x)= M(x)*A(x)$. Issue here is $A(x) = C_1+C_2* x $ where $C_1,C_2 $ has dimension $3 \times 3$. And x is a scalar variable Doubt What is M(x)? Can any one give ...
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2answers
65 views

Matrix exponential Differentiation

We have the equation $e^X = \sum_{k=0}^\infty{1 \over k!}X^k.$, where X is a matrix of dimension $3 \times 3$ . Now I have a function $f(x)=C_1x+C_2*\frac{x^2}{2} $ where $C_1,C_2,f(x)$ has ...
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0answers
38 views

Derivatives, help please.

${E = - \cfrac{\sum\limits_{c}^C \log P(C)Y}{N}}$ where ${\log P(C) = I_c - \log \sum\limits_{c}^C \exp\left(I_c - \max_c\left(I_c\right) \right)}$ ${I_c = WO}$ ${W}$ is ${C \times N.Hid}$ weight ...
1
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2answers
26 views

Calculus Implicit Differentiation and Concavity

Consider the relation $4x^2 - y^2 = -2$ (a) Use implicit differentiation to calculate $dy/dx$ and find all critical points of the curve. (b) Calculate the second derivative and determine the ...
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2answers
46 views

Proof of application of Mean Value Theorem

Two bicyclists begin a race at 8:00AM. They both finish the race 2 hours and 15 minutes later. Prove/explain that at some point during the race, the bicyclists are traveling at the same velocity. So ...
4
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3answers
215 views

How to differentiate $\lim\limits_{n\to\infty}\underbrace{x^{x^{x^{…}}}}_{n\text{ times}}$? [duplicate]

Let $$f(x)=\lim\limits_{n\to\infty}\underbrace{x^{x^{x^{...}}}}_{n\text{ times}}$$ Is it possible to find $f'(x)$. If yes, please show all steps.
3
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1answer
61 views

Stuck trying to prove that $e^{-x^{-2}}$ is $C^{\infty}$ [duplicate]

This is Spivak's Calculus on Manifolds ex. 2-25, he says Define $f:\mathbb{R}\to \mathbb{R}$ by $f(x) = \left\lbrace \begin{array}{l} e^{-x^{-2}} &\text{ if } x \neq 0\\ 0 ...
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2answers
39 views

Problem related to Mean Value Theorem

I found out a question that I can't figure out a way to solve it. Plz can anyone help me. Question is, Prove that $\exists\,C\in(0,\pi/4)\,\mathrm{s.t.}\,\tan(\pi/4+C)=3/C$ I know this should be ...
3
votes
4answers
84 views

Implicit Derivative approaches

Sorry for my excessive verboseness... Here's the equation as given: $$x = 10 + \sqrt{x^2 + y^2}$$ Here are my direct implicit steps without modifying original equation: $$\eqalign{ \dfrac{\mathrm ...
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0answers
35 views

Solving system of differential equations

I have a system of differential equation to solve. Any suggestions regarding closed form or numerical method is welcome with great respect. This equation is from dynamic equation of a curve. Let us ...
0
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1answer
16 views

Find the equation of a line tangent at a specific point

I have to find an equation for the line tangent to the graph of $\large\frac {\sqrt{x}}{6x+5}$ at the point $(4,f(4))$, and write it out in the form of $y=mx+b$ Using the quotient rule I get.. ...
1
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3answers
54 views

surjective, but not injective linear transformation

$T$ is a transformation from the set of polynomials on $t$ to the set of polynomials on $t$. So, the input to $T$ should be a polynomial, and the output should be some other polynomial. Two common ...
1
vote
1answer
35 views

Differentiating Integrals

This problem appears as example 2d of Chapter 5 in "A First Course in Probability - Ross, 8th ed." Suppose that if you are s minutes early for an appointment, then you incur the cost cs, and if you ...
2
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3answers
63 views

Using the Chain Rule to prove trig derivatives

I'm having trouble with this problem, I'm not sure how to tackle it and I was wondering if somebody could set me on the right path. The problem is as follows: Use the Chain Rule to show that if ...