1
vote
2answers
21 views

implicit differentiating equation with $\cos$

I need help getting $\frac{d^2y}{dx^2}$ for $y−\cos y=2x$ Someone answered and got $(1+\sin y(x))3+4\cos y(x)$ but i was unable to follow their steps and didnt get how to do it. any HELP?
1
vote
1answer
41 views

Need help with implicit differentiation

hi i need help on finding the $\dfrac{d^2 y}{d x^2}$ for $x^6-y^6=14$ i got $$\frac{5x^4(y^6-x^6)}{y^{11}}$$ but im not sure if its right or not also i am completly stuck on getting $\dfrac{d^2 ...
1
vote
1answer
33 views

Derivative of a minimum

The expression, $e=\left(x(t,w)-c_x\right){}^2+\left(y(t,w)-c_y\right){}^2$, has a local minimum with respect to $t$ at some $t_0(w)$. Now what does $t_0'(w)$ look like?! $x,y\in C^2$ with respect to ...
1
vote
0answers
35 views

Multiplying partial derivatives

I am trying to understand what happens when I have a continuous differentiable function $f$ on $\mathbb{R}^n$ such that $f$($x_1,x_2,...x_n$) = 0. What is the significance of the product: ...
4
votes
2answers
99 views

Multivariable calculus - Implicit function theorem

we are given the function $F: \mathbb R^3 \to \mathbb R^2$, $F(x,y,z)=\begin{pmatrix} x+yz-z^3-1 \\ x^3-xz+y^3\end{pmatrix}$ Show that around $(1,-1,0)$ we can represent $x$ and $y$ as functions of ...
2
votes
0answers
23 views

Implicit differentiation and rules

I'm supposed to write the rules used for some differentiable functions. I got all of them correct except for the last one which is $d(x^c)$. I put in $cx^{c-1}$ because I thought it was the power ...
0
votes
0answers
22 views

$x$-coordinates of points where tangent line is horizontal or vertical. Using implicit differentiation

For the implicit equation $x^3 + y^3 - xy^2 = 8$ Determine the exact x-coordinates of all points where the tangent line is horizontal or vertical I figured out $\dfrac{dy}{dx} =\dfrac{y^2 - 3x^2}{ ...
0
votes
1answer
45 views

The normal line intersects a curve at two points. What is the other point?

The line that is normal to the curve x^2 + xy - 2y^2 = 0 at (4,4) intersects the curve at what other point? I can not find an example of how to do this equation. Can someone help me out?
0
votes
1answer
29 views

implicit differentiation using trigonometry functions

xcos(4x+3y)=ysinx I have been stuck on this problem for the longest. I have the answer but I don't know how to get to it. I have used the product and chain rule ...
2
votes
2answers
49 views

Use implicit differentiation to find derivative

$$x\sin(4x+5y)=y\cos(x)$$ I am trying to use implicit differentiation to find dx/dy for this problem but the answer i keep getting is $$4x\cos(4x+5y)=-y\sin(x)$$ and I am stuck.
-4
votes
2answers
102 views

really hard calculus 1 problem. implicit [closed]

If $x^3 + y^3 = 26$, find the value of $d^2y/dx^2$ at the point (-1,3). The value at $d^2y/dx^2$ at the point $(-1,3)$ is _? (type a simplified fraction) I started out by finding the derivative of ...
1
vote
1answer
31 views

Find derivative of a trig function.

If $y=\csc(xy)$, then find $y'$ in respect to $x$ $y'=-\csc(xy)\cdot \cot(xy)\cdot(xy)'$ $(xy)'=(x)'(y)+(x)(y)'$ $(xy)'=y+xy'$ $y'=-(y+xy')[\csc(xy)\cdot\cot(x)]$ AND, that's where I get lost. So ...
3
votes
2answers
78 views

Finding the second derivative; What am I doing wrong?

Original Question: $xy+y-x=1$ Find the second derivative; $d^2y\over{dx^2}$$(xy+y-x=1)$ We are allowed to use either notation as far as I know: ${dy\over{dx}}$ or ${y'}$. Because ...
2
votes
2answers
47 views

Implicitly differentiate $e^y \cos(x) = 1 + \sin(xy)$

I can differentiate one side of the equation, but I dont know how to deal with sin(xy)
1
vote
5answers
52 views

Finding the Derivative of a Derivative

Let $x^3+y^3=9$. Find $y''(x)$ at the point $(2,1)$. I keep getting $3x^2+(3y^2)y'=0$ as the first derivative then simplify that down to $-3x^2/(3y^2).$ But after that I keep getting ...
-1
votes
2answers
47 views

Use implicit differentiation to find an equation of the tangent line to the curve

$$x^2+xy+y^2=3, (1,1)$$ I got the derivative as.. $$\frac{2x-2}{x+4}$$ But when I plug in the points I get the equation $y=x/2+2$ which is wrong. Is my derivative wrong? Or am I making a mistake ...
1
vote
2answers
125 views

Implicit form of general equation

Find, in implicit form, the general solution of the differential equation: $$\frac{dy}{dx}= \frac{2y^4e^{2x}}{3\left(e^{2x}+7\right)^2}$$ I am struggling to make any sense of this. What I have ...
-1
votes
2answers
65 views
-1
votes
2answers
66 views

Find the slope of the tangent line $\ln(3y-5)+x=y^2$ at $(4,2)$ [closed]

Find the slope of the tangent line $\ln(3y-5)+x=y^2$ at $(4,2)$. I need help with differentiating the ln part but a complete step by step answer would help.
-1
votes
2answers
57 views

Differential Calculus, Slope at a Given Point [closed]

If $$3x^2 + 2xy + y^2 = 2$$ then what is the value of $dy/dx$ when $x = 1$?
2
votes
3answers
190 views

Intersection of normal to the curve

The line that is normal to the curve $x^2+3xy-4y^2=0$ at $(6,6)$ intersects the curve at what other point? If I implicitly differentiate this curve, I will get the equation of the slope: ...
0
votes
2answers
133 views

Finding the tangent line(s) to a curve

first time poster so sorry if I'm doing something wrong. "Consider the closed curve in the xy-plane given by $2x^2 - xy + y^3 + x = 9$. Find equation(s) of all tangent lines to the curve at $y = ...
2
votes
3answers
74 views

How to get the derivative of $(\ln(x))^{\sec(x)}$?

How do you get the derivative of $(\ln(x))^{\sec(x)}$? I know that the derivative of $\ln(x)$ is $\frac 1x$ but what happens when you take it to an exponent of $\sec(x)$?
1
vote
2answers
132 views

Tangent line to the curve $x^3+xy^2+x^3y^5=3$

Does the tangent line to the curve $x^3+xy^2+x^3y^5=3$ at the point $(1,1)$ pass through the point $(-2,3)$? (using implicit differentiation) I got the implicit differentiation as ...
0
votes
1answer
33 views

Negative derivative

If f is a differentiable function on R such that f(−x) = −f(x), for all x ∈ R, then could you explain why f′(−x)=f′(x) ?? An example would be so helpful! Thank you!
1
vote
1answer
125 views

Implicit Differentiation

Use implicit differentiation to find the points where the circle defined by x2+y2−2x−4y=−1 has horizontal tangent lines. List your answers as points in the form (a,b). 1. Find the points where the ...
2
votes
1answer
53 views

Using implicit differentiation to solve a function and stuck at factoring out y'.

So here is the question: $$ \tan^{-1}\left(\frac{2x}{y}\right)=\frac{\pi x}{y^2} $$ When I solved it implicitly I got (with much pain in formatting it on this site :P): $$ y^2=\pi ...
1
vote
2answers
49 views

Implicit Differentiation of the following equation

$$4x^3 + x^2y - xy^3 = 4$$ This is what I have so far: $$(2xy + x^2 y') - (y^3 + 3xy^2 y') = -12x^2$$ Should I bring everything but the y primes over to the right side by dividing it? I'm not so ...
0
votes
1answer
22 views

Implicit differentiation: $\mathrm d\left(\frac{t+2}{t-3}\right) / \mathrm d\left(\frac{3t+1}{t-4}\right)$

So I have: $$y=\frac{t+2}{t-3},\qquad x=\frac{3t+1}{t-4}$$ What is $\dfrac{\mathrm dy}{\mathrm dx}$ when $t=1$? I got $\dfrac{45}{52}$ but wanted to check the answer.
2
votes
0answers
75 views

Relating $x$ to $\frac{dx}{dt}$ in a right triangle.

I have a right triangle with sides of $x$ and $y$. I know $y$ is a constant (500) and that $\frac{d \theta}{dt}$ (where $\theta$ is the angle opposite from side $x$) is also constant ($8\pi$ rad/s). I ...
1
vote
1answer
92 views

Implicit function theorem “submersion version”

In class we learned the following variant of the Implicit Function Theorem: Suppose $f:U \to \mathbb{R}^{n-k}$, where $U \subseteq \mathbb{R}^n$, is such that $Df(p)$ has full row rank for all $p \in ...
2
votes
1answer
69 views

question about MIT calc 1 implicit diff video

The implicit solution to $y^4+xy^2-2=0$ is written on the board as $$ y^{\prime} = \frac{-y^2}{4y^3+2xy}$$ did I miss something, but can't you factor out a y? so it should be $$y^{\prime} = ...
2
votes
3answers
73 views

Implicit differentiation question

Given that $x^n + y^n = 1$, show that $$\frac{d^2y}{dx^2} = -\frac{(n-1)x^{n-2}}{y^{2n-1}}$$. I found that $\displaystyle nx^{n-1}+ny^{n-1}\frac{dy}{dx} = 0$ so that $\displaystyle ...
0
votes
1answer
40 views

Implicit derivation help? Please give me a hint (possibly a line #)

ok so i am having trouble with finding the implicit derivative for this problem. I am doing it on an ipad and here is a screen shot of my work. A hint would better than a solution! Thanks.
0
votes
1answer
67 views

Translation from Spanish - Simple differentiation exercise

Could anybody please translate this exercise into English? A friend of mine sent me the translation via Facebook but I still don't understand why I have to first do the logaritmization of both sides ...
1
vote
0answers
48 views

Implicit function theorem and discrete changes

I have a rather complex expression $F(x,y)=0$, which implicitly defines $y$, and can find out how $y$ response to a marginal change in $x$ via the implicit function theorem: ...
1
vote
1answer
171 views

Derivative of $x\sqrt{1+y}+y\sqrt{1+x}=0$ [closed]

$$x\sqrt{1+y}+y\sqrt{1+x}=0$$ To prove $$\frac{dy}{dx}=-\frac{1}{1+x^2}$$ I tried shifting $y\sqrt{1+x}$ to RHS and squaring and then finding the derivative but it still gives complicated quadratic ...
1
vote
3answers
216 views

Help with implicit differentiation: $e^{9x}= \sin(x+9y)$

Find $\;\dfrac{dy}{dx}\;$ given $\;e^{9x}= \sin(x+9y)$ the answer is $\;\displaystyle\frac{e^{9x}}{\cos(x+9y)}- \frac{1}{9}$. Can you show the process of how this is worked? thanks.
8
votes
3answers
284 views

Given that $x = 4\sin \left( {2y + 6} \right)$ find dy/dx in terms of x

My attempt: $\eqalign{ & x = 4\sin \left( {2y + 6} \right) \cr & {{dx} \over {dy}} = \left( 2 \right)\left( 4 \right)\cos \left( {2y + 6} \right) \cr & {{dx} \over {dy}} = 8\cos ...
1
vote
1answer
106 views

How to find a directional derivative of an implicit function?

it's not my homework, I just want to find out how to find a directional derivative of an implicit function. I know what is a directional derivative and how to find it when I have a function in normal ...
4
votes
2answers
120 views

Help finding the 3rd derivative

If $x^2-xy+2y^2=\frac{a^2}{7}$, find $y'''$. For our 1st derivative we got $$y'=\frac{2x-y}{x-4y}.$$ For the second derivative we got $$y''=\frac{14x^2-14xy+28y^2}{(x-4y)^3}.$$ And for the final ...
1
vote
1answer
74 views

Highest derivatives of implicit function

I am learning to use the implicit function theorem (IFT) and met recently the following problem: Let $F(x,y)=x+y+x^5-y^5$. The given equation defines a smooth function $\phi:U\rightarrow \mathbb{R}$ ...
5
votes
4answers
580 views

Can someone give me a deeper understanding of implicit differentiation?

I'm doing calculus and I want to be an engineer so I would like to understand the essence of the logic of implicit differentials rather than just memorizing the algorithm. Yes, I could probably ...
1
vote
2answers
64 views

Finding derivatives using implicit differentiation

Find $y'(x)$ for $y=y(x)$ if: a) $\sin(xy) -e^{xy}-x^2y=0$ b) $x^y+y^x=0$ So the formula for these types of functions is $dx/dy = -F_x(x,y)/F_y(x,y)$. How to apply this?
6
votes
2answers
99 views

Find the derivative in term of $x$ and $y$.

$\frac{\mathrm{d}y}{\mathrm{d}x} = 3x + 2y + 1$ Find $\frac{\mathrm{d}^2 y}{\mathrm{d}x^2}$ in term of $x$ and $y$. I get $3+2y^{\prime}$ for the answer. Lost upon how to get the answer in terms ...
1
vote
3answers
155 views

Implicit Differentiation Problem???

PROBLEM: Heat flows normal to isotherms, curves along which the temperature is constant. Find the line along which heat flows through the point $(2,5)$ when the isotherm is along the graph of ...
0
votes
2answers
41 views

Implicit Derivative help

The problem I'm working on is $\sin( x + y ) = 2x-2y$. If anybody could give a step by step solution I would be very appreciative. I'm trying to find the derivative of y
0
votes
2answers
81 views

Implicit derivative of $(x - y)^2 = x + y - 1$

I changed the function from: $(x - y)^2 = x + y - 1$ to: $(x^2) - (y^2) - x - y = -1$ All I did was move the variables to one side. When moved, I get $\displaystyle \frac{dy}{dx} = \frac{2x - ...
0
votes
0answers
371 views

Derivatives Related Rates Ladder Problem

The exercise with solution is: $$$$ The way I tried to solve it is: $x^2 + y^2 = 15^2$ $$$$ $dx = t\frac{dx}{dt} = 12\frac{1}{4} =3$ $x_{before} = 10$ $x_{after} = x_{before} - dx = 10 - 3 = 7$ ...
1
vote
1answer
98 views

Differentials and implicit differentiation

Consider this example. Suppose $x$ is a function of two variables $s$ and $t$, $$x = \sin(s+t)$$ Taking the differential as in doing implicit differentiation [1], $$dx = \cos(s+t)(ds+dt) = \cos(s+t)dt ...