3
votes
1answer
41 views

Finding derivative form the definition

I want to find the derivative of the function $f:\mathbb R^n\to \mathbb R^m$ at a point $x_0\in \mathbb R^n$, where $f(x)=c\in \mathbb R^m$, is a constant function. What I did is as follows: If $f$ ...
0
votes
3answers
63 views

Can you factor before finding derivative?

Say the function is $y=\frac{x^2-1}{x-1}$ Can you factor functions before finding the derivative or does that not work?
1
vote
1answer
30 views

Is it possible to have a inflection on a vertical asymptote?

I found the derivative of a function to be f'(x)=8/x^3 and thus its second derivative as f''(x)=0/3x^2. After setting the second derivative to zero and doing the substitution into the parent function, ...
2
votes
3answers
87 views

Can an inflection exist if there's no max/min?

Very quick question: if a function doesn't have a maximum nor minimum, can it still have a point of inflection? I believe that these two go hand in hand and without one you can't have the other but ...
1
vote
6answers
47 views

Using Chain Rule and Product Rule to find derivative

I have to find the derivative of the following function: $$f(x) = (x^3+ 4)(4x^5 + 2x − 5)^{1/2}$$ To start solving this, I've dissected the equation and realize that I must use the product and chain ...
1
vote
1answer
23 views

How is the power rule applied to whole numbers

For the following function, how does the $+1$ become $0$ when finding its derivative via the power rule? Original function: $f(x) = 6x^2 − 4x^{-1} + 5x^{-2} − 2x + 1$ Derivative: $f '(x) = 12x + ...
0
votes
1answer
31 views

Total derivative proof [closed]

The wikipedia article does not prove it http://en.wikipedia.org/wiki/Total_derivative Neither the top articles in google search. Could somebody help me proving it? I've found this: ...
-1
votes
1answer
12 views

Equation of a line with a positive gradient [closed]

Two straight lines passing through the point (0,2) are tangent to the graph of the function y=1-x^2. Find the equation of the line with a positive gradient.
1
vote
1answer
34 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 ...
0
votes
2answers
25 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) ...
-1
votes
2answers
49 views

Differentiability at x=0 [closed]

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
votes
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 ...
0
votes
1answer
45 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!
0
votes
2answers
23 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: $y'(x) = 4x^3-500$ ...
0
votes
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
vote
2answers
61 views

Help me check my homework

I have $$ h_\theta(x) = \frac 1 {1+e^{-\theta x}} $$ I need to get $ \frac d {d\theta} h_\theta(x) $. Here are my work. $$\begin{eqnarray} \frac d {d\theta} h_\theta(x) &=& \frac d ...
2
votes
3answers
178 views

Derivative and integral of the abs function

I would like to ask about how to find the derivative of the absolute value function for example : $\dfrac{d}{dx}|x-3|$ My try:$$ f(x)=|x-3|\\ f(x) = \begin{cases} x-3, & \text{if }x \geq3 \\ ...
0
votes
1answer
35 views

Comfirmation of third derivative of symbolic equation including summation

With previous help I was able to find the first derivative of an equation for a work project. Now I'm after the second and third derivative, for use in a program to find the maximum (Which I must do ...
-1
votes
2answers
72 views

I need help solving this related rates equation.

I need help answering the following question and I'll show you what I have. ! $$x=20,y=\sqrt{2100},z=50, \frac{dy}{dt}=30$$so differentiating $(20)^2+y^2=z^2$ $$2y\frac{dy}{dt}=2z\frac{dz}{dt}$$ And ...
0
votes
1answer
27 views

Average rate of change over the given interval?

Find the average rate of change for the following functions please. I'm facing problems in these. $s=2t^3-5t+7$ interval from $t=1$ to $t=3$ $h=\sqrt{2t}-7$ interval from $t=8$ to $t=8.5$
1
vote
3answers
91 views

Derivative in calculus $f(t)= 7\sinh(\ln t)$

How to find the derivative of this function $$ 7\sinh(\ln t)?$$ I don't know from where to start, so i looked at it in wolfram alpha and it was saying that the $$ 7((-1 + t^2) / 2t) $$ I did not get ...
0
votes
1answer
21 views

Maximize area of a rectangle between parabola and a line

I was given a task to maximize the area of a rectangle that can be inscribed between parabola $y=1-x^2$ and a line $y=0$ such that one side of the rectangle lies on the $x$ axis. My idea is to somehow ...
0
votes
4answers
55 views

Calculus about derivative

How to solve this derivative? $$\large p(t) = 3e^{{-2e}^{2t}}$$ It looks weird to have two exponents instead of one. I tried to solve it but i got stuck.
3
votes
1answer
48 views

Finding limit of cube root [duplicate]

I'm trying to evaluate this limit, but I don't think it's coming out correctly. Could someone please offer me some assistance? Evaluate limit analytically $$\lim_{h\to 0}\frac{\sqrt[3]{x + h} - ...
0
votes
1answer
23 views

finding velocity from a table

I have a homework question I am seeking an alternative solution to. Basically, the question is... "The table provided below shows the position of a particle S, at several times, t. as the particle ...
1
vote
1answer
40 views

Rates of change question?

A boat is observed from top of a $100\ \text m$ high cliff. The boat is travelling towards the cliff at a speed of $50\ \text{m/min}$. How fast is angle of depression changing when angle of ...
1
vote
1answer
16 views

Derivative of exponential function

1) $f(t) = (\ln 5)^t$ what is the $f'(t)$? I tried $t\ln(5)$ but it was wrong. 2) $f(x) = x^{\Large π^6} + (π^4)^x$ This one I did not attempt in it because I find it confusing little bit.
1
vote
4answers
60 views

Need an example of piece wise function continuous but not differentiable

I Need an example of piece wise function continuous but not differentiable. One of the functions has to be trigonometric and the other has to be exponential. Please
4
votes
1answer
37 views

Prove increase of expected value

I am trying to prove the following: For $x$ distributed on $X=[a,b]\subset \mathbb{R}^+$ with the cumulative distribution function $F(\cdot)$ s.t. $F'(x)=f(x)>0\ \forall x\in X$: $E[x\mid ...
0
votes
1answer
24 views

Slope of a tangent line for curve

Hi I have a quick question I'm hoping someone could help me iron out. Below is a homework question I'm working on, and I need help with part (b). The answer it seems to me is "less than", and not ...
3
votes
0answers
35 views

Prove Differentiation Multivariable

Given $f(x,y) = \frac{ xy^2}{x^2 +y^2}$ From defintion we know it is differentiable if: $\lim_{h\to 0}\frac{F(X+h)-F(X)-c*h}{|h|}$ exists, where $c$ is the gradient of the function. I have ...
3
votes
3answers
87 views

Show that $f(x) = x\sin(1/x)$ is Differentiable everywhere where $x\ne0$.

I have to show that $f(x)= x\sin(1/x)$ is continuous everywhere differentiable everywhere where $x\ne 0$. I can show the continuous property, and how it is not differentiable when $x=0$, but how ...
1
vote
2answers
73 views

Prove that a differentiable function $f$ with $f(x+1)=f(x)$ has at least two points in $[0,1]$ such that $f ' (x) =0$.

Prove that a differentiable function $f$ with $f(x+1)=f(x)$ has at least two points in $[0,1]$ such that $f ' (x) =0$. I used Mean value theorem to obtain one such point in $[0,1]$ , but i am not ...
1
vote
2answers
67 views

Integrable function on $[0,2]$ and its antiderivative

I got this question: Let $f$ be the integrable function defined on the interval $[0,2]$ by the rule: $f(x)= \begin{cases} 4x^3 & \text{if $0 \leq x \leq 1$} \\ x^2+2 & \text{if $1<x \leq ...
1
vote
2answers
51 views

Derivative of $\frac{\sin \coth x}{\csc \sqrt{e^{\log x}}}$

Derivative Problem: Hello, Ciao tutti, Buenos dias! I am trying find derivative with respect to x of function: $$ G(x)=\frac{\sin \coth x}{\csc \sqrt{e^{\log x}}}. $$ Derivativative rule for general ...
2
votes
2answers
41 views

An object is travelling in a straight line. Its distance, s meters, from a fixed point at time t seconds is given by the expression

$$s=t^3−t^2−6t$$ a) Find ds/dt when t=3 and interpret this result. b) Find d^2s/dt^2 when t=3 and interpret this result. c) Find the time in seconds when the velocity is 2m/s (d) Using the ...
0
votes
2answers
66 views

Values of $x>0$ of a curve

I got the following task: A curve has the equation $$ y = x^{\frac{3}{2}} + \frac{48}{x} $$ for values of $x > 0$. Find the coordinates of the turning point of the curve. By ...
2
votes
3answers
48 views

Limits of trig functions

How can I find the following problems using elementary trigonometry? $$\lim_{x\to 0}\frac{1−\cos x}{x^2}.$$ $$\lim_{x\to0}\frac{\tan x−\sin x}{x^3}. $$ Have attempted trig identities, didn't help. ...
1
vote
4answers
60 views

Differentiate $y=4\,e^{\cos2x}$

I do not know what to do for this question $$ y=4\,e^{\cos2x}$$ Can anyone show me or give me an example? I think I should be using the chain rule but not $100\%$ sure how to break up the question.
2
votes
1answer
46 views

Smoothness of $f(x)/(1+|f(x)|)$ where $f \in C^1(E)$ for $E$ an open subset of $\mathbb{R}^n$

(a) Show that if $E$ is an open subset of $\mathbb{R}$ and $f \in C^1(E)$ then the function $$F(x) = \frac{f(x)}{1+|f(x)|}$$ satisfies $F \in C^1(E)$. (b) Extend the results of part (a) to $f \in ...
-1
votes
1answer
16 views

Oscillating Spring & Rates of change

How to solve? Are they asking for: instantaneous rate of change: $\frac{d}{dt}h(t)=2.5$ and solve for value of $t$ or when $\frac{d}{dt}h(t_1)$ where $t_1$ is when $h(t)=2.5$ but both methods ...
2
votes
3answers
277 views

Differentiate the following function

$$y = \sqrt {\sin x} = (\sin x)^{\frac 12}$$ \begin{aligned} {dy \over dx} & = \frac 12 (\sin x)^{-\frac {1}2}{d\over dx} \sin x \\ & = \frac 12 (\sin x)^{-\frac 12} \cos x \\ & = ...
0
votes
1answer
39 views

Differentiate the following functions

Let $$y(x)= 4 x^3 e^{2x},$$ then $$y'(x) = 4 \times 3 \, x^2 e^{2x} + 4 \, x^3 \times 2 e^{2x} = 12 \, x^2 e^{2x} + 8 \, x^3 e^{2x}$$ Does this look correct?
2
votes
1answer
28 views

Newton's binomial for matrices that don't commute?

I'll give a bit of background info as to why I'm asking. I need to find the directional derivative of $f(A)=A^m$ where $m>0$ and $A$ is an $n$ by $n$ matrix with real entries. I want to do this ...
2
votes
1answer
37 views

How to find the differential of this function

we are given the function $f: \mathbb R^n \setminus \{0\} \to \mathbb R^n$ defined by: $f(x) = \frac{x}{|x|}$ Find $Df(a)$. What I did: I tried working this out from the definition. the ...
-1
votes
2answers
87 views

Find the gradient of the curve $y = \sin x$ at $x = 0$. [closed]

Not sure how to even approach this question, can anyone help me?
1
vote
1answer
51 views

Computing the derivative of an integral

There are similar questions on the same topic, yet I could not figure out why the following equation (taken from an economics solution manual) holds: $$ \frac{\partial}{\partial C(i,j)} ...
0
votes
0answers
27 views

Questions from a calculus assignment about a function [duplicate]

Can anyone guide me through this problem? Let $f(x) = \lvert 4-x^2 \rvert$, $-4\le x\le 1$. Sketch (I have completed this part). Rewrite $f$ as a piecewise function. Give the range of $f(x)$. Use ...
6
votes
3answers
156 views

optimal way to approximate second derivative

Suppose there is a function $f: \mathbb R\to \mathbb R$ and that we only know $f(0),f(h),f'(h),f(2h)$ for some $h>0$. and we can't know the value of $f$ with $100$% accuracy at any other point. ...
1
vote
1answer
17 views

How to find the values of constants when there is one stationary point, no stationary point, and determining the maximum number os stationary points.

b) values of x is when f'(x) = 0 c) how do i solve this without using common sense and knowing that if a=0 there will be no turning points/inflections d)how do i solve this? e) max number of ...