For questions on finding and evaluating derivatives when a function is defined implicitly.

learn more… | top users | synonyms

1
vote
2answers
19 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?
2
votes
0answers
27 views

Implicit Differentiation Proper Answer?

I'm studying for my calc final tomorrow, and am going through some practice questions and I'm not sure if the solution is wrong or I'm just miss understanding. The question is about finding a tangent ...
0
votes
1answer
24 views

Inverse/implicit functions

How does one prove that there exists a differentiable real-valued function $y(x)$ in some neighborhood of the point $x = 0$ such that $$x = e^{-y(x)}y(x)$$ for all $x$ in that neighborhood? ...
2
votes
2answers
35 views

Implicit Differentiation usage of $\frac {dy}{dx}$

Why, after differentiating $y$ on one side of the equation, is $dy/dx$ added? As clarification an example I will provide an example: Implicitly differentiate $y^2 = x$. You get $$2y\frac {dy}{dx} = ...
0
votes
0answers
39 views

Why is $\frac {dy}{dx}$ treated as a fraction? Plus an implicit differentiation question. [duplicate]

Why is $\frac {dy}{dx}$ treated as a fraction? I always thought that it is just notation for the derivative of $y$ with respect to $x$, but when it comes to implicit differentiation and integration ...
1
vote
1answer
39 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
96 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 ...
5
votes
1answer
78 views

Multivariable calculus - find derivative using implicit differentiation

Short simple question which i managed to solve partially. we are given the equation $x^2+y^2-z^2+xz-yz-1=0$. Show using the implicit function theorem that this equation sets in the neighborhood of ...
1
vote
2answers
28 views

Chain rule in multivariable calculus

I am studying notes from seminar and I don't quite understand some steps. We were evaluating implicit function $f(x,y)=e^{xy}+\sin y +y^2 =1 $ at point $[2,0]$. After checking the conditions we ...
0
votes
1answer
20 views

Related Rates Word Problem: Shadow of a falling rock

So I'm doing my online homework on related rates, which is tedious and confusing to me as it is, and I run into this problem with no idea on how to do it. Can anyone help me understand the steps ...
0
votes
1answer
27 views

Planes going in directions at different heights

One plane is flying due east straight and level at 30000 feet and at 420 mi/h. a second plane flies due north at 40560 feet at 480mi/h. The second plane crosses above the flight path of the first ...
0
votes
1answer
23 views

Calculus implicit differential

So i am here with my question , Question asks $(x-y)^2 = x + y - 1$. $2 (x-y) (1- y') = 1 + y'$ I am a little confused when it comes to right here, can anyone clarify a little, I know the step that ...
2
votes
0answers
22 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 ...
1
vote
2answers
12 views

Implicit differentiation at a given point

I was given this problem on my online homework, but I'm getting stuck when trying to get the $dy/dx$ term on one side. The question is: "For the equation given below, evaluate $dy/dx$ at the point ...
0
votes
1answer
35 views

Implicit Derivative

I did lots of calculation, but it just only going to be nothing but mess. If anyone could help me, thanks.
1
vote
0answers
18 views

Prove an implicit function solves an O.D.E

Let $\Phi(u,v)$ differentiable on the plane. a. which condition should $$\Phi(x+az,y+bz)=0\quad(a,b\in\mathbb R)$$ satisfy in order to define a function $z=z(x,y)$? b. Prove that ...
0
votes
2answers
55 views

How to implicitly differentiate $x \sin x = y(1 + \cos y)$?

If $x \sin x = y(1 + \cos y)$, find $y'$ at $(\frac{\pi}{2}, \frac{\pi}{3})$. Please show each step.
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
41 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
3answers
40 views

How do I implicit differentiate this equation?

The task is to determine the equation for the tangent line at the point $(-2,1)$ to the curve below. I would like to know if I am solving this the right way and also if the answer is right (I don't ...
0
votes
1answer
28 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
48 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
98 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
votes
1answer
71 views

Calculus 1: Implicit differentiation [closed]

If $x^3+y^3=7$, find the value of $\dfrac{d^2y}{dx^2}$ at the point $(-1,2)$. The value of $\dfrac{d^2y}{dx^2}$ at the point $(-1,2)$ is? This one is really tough
1
vote
1answer
28 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
77 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 ...
0
votes
1answer
26 views

implicit differentiation with related rates

If a snowball melts so that its surface area decreases at a rate of $1\ cm^2/min$, find the rate at which the diameter decreases when the diameter is 10 cm. So I know that the surface area of a ...
2
votes
1answer
39 views

Showing that an implicitly defined function is analytic on $(0,\infty)$

I would like to know some suggestions as to how to approach this problem: Let $h\geq 0$, $\beta \in \mathbb{R}$, and denote by $f(h)$ the largest solution of $$\tanh (2\beta x + h) = x. $$ Prove ...
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
51 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
42 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
60 views

Rate of descent of a hot air-balloon

A rope is attached to the bottom of a hot air-balloon that is floating above a flat field. If the angle of the rope to the ground remains at 65 degrees and the rope is pulled in at 5 ft/s, how quickly ...
0
votes
2answers
45 views

How do I find dy/dx by implicit differentiation?

Find $\displaystyle \frac{dy}{dx}$ by implicit differentiation. $\tan(x+y)=x$ So far, I got to $\displaystyle \sec^2(x+y) \left(1+\frac{dy}{dx}\right) = 1$ but then im lost.. can someone please ...
2
votes
3answers
89 views

$\frac {\operatorname d\!y}{\operatorname d\!x}$ for $\sqrt{xy}=1$

To find $\displaystyle \dfrac {\operatorname d\!y}{\operatorname d\!x}$ for $\sqrt{xy}= 1$: $$\dfrac{\sqrt y}{2\sqrt x}+\dfrac{y'\sqrt x}{2\sqrt y}=0\\ \dfrac{y'\sqrt x}{2\sqrt y}=\dfrac{-\sqrt ...
2
votes
2answers
34 views

Differentiating this implicit expression?

I am given: $$\tfrac{1}{4}(x+y)^2 + \tfrac{1}{9}(x - y)^2 = 1$$ Using the chain rule, and factoring out $y'$, I'm left with: $$y' \left(\tfrac{1}{2}(x+y) - \tfrac{2}{9}(x-y)\right) = 0$$ Now I ...
2
votes
1answer
84 views

Implicit function, real analysis homework question

Consider the equation $xe^{y}+ye^{x}=0$ (a) Prove that this equation defines $y$ as a $C^{\infty}$ function of $s$ in a neighborhood of $(0,0)$ (b) Ley $y=g(x)$ be this implicitly defined function. ...
2
votes
2answers
98 views

General and particular solution of differential equation

1) I need to find, in implicit form, the general solution of the differential equation $$\frac{dy}{dx}=\frac{2y^4e^{2x}}{3(e^{2x}+7)^2}$$ 2) I then need to find the corresponding particular solution ...
1
vote
2answers
117 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 ...
0
votes
1answer
32 views

Slope of line tangent to function at point.

I hope the picture's quality isn't too bad, but the question was slope of line tangent to $y^2 + (xy +1) ^3 = 0$ at point $(2,-1)$. I tried two ways where one was trying to find the derivative ...
0
votes
1answer
21 views

Using implicit differentiation, verify that $u=f(x-tu)$ satisfies $\frac{\partial u(x,t)}{\partial t}+u(x,t)\frac{\partial u(x,t)}{\partial x}$.

Using implicit differentiation, verify that $u=f(x-tu)$ satisfies $\frac{\partial u(x,t)}{\partial t}+u(x,t)\frac{\partial u(x,t)}{\partial x}$. Could someone explain how implicit differentiation ...
0
votes
1answer
30 views

Solve the derivatives of a certain implicit function

I have a function which looks like: $y = f (x_{1}, g(x_1, y))$. I want to express the cross-partial of $g$ w.r.t $x \;and \; y$ in terms of the function or derivatives of $f$. Here is how I did: ...
1
vote
1answer
32 views

Checking the solution of a first order pde

I need some help with this exercise. Given the following pde: $ \begin{cases} u_t + b(u)\cdot u_x=0\\[6pt] u(x, 0) = u_0(x) \end{cases} $ I have to check that its solution is $u(x, ...
0
votes
0answers
16 views

Finding the second derivative of a implicit function of two variables

Given a function $z:\Bbb R^2 \rightarrow\Bbb R$ and $F:\Bbb R^3 \rightarrow \Bbb R$ (both are $C^2$) and knowing that $F(x,y,z(x,y))=0$ and $\frac{ \partial F}{\partial z}(x,y,z(x,y))\ne 0$ find ...
1
vote
0answers
116 views

How to prove orbit periodicity in some conservative systems?

Good afternoon, I have some trouble proving periodicity with a conservative system. The problems is that I don't know how to make a formal demonstration although I can see it quite true. I have the ...
-1
votes
2answers
64 views
5
votes
2answers
78 views

What is the slope of the tangent at $(0,0)$ on the curve $x^2 y^2 = 4 x^5 + y^3$

This question is arising from the answer to another one: How find this equation integer solution: $x^2y^2=4x^5+y^3$ . For $x < 27$ and $y > -243$ , the basic equation $x^2 y^2 = 4 x^5 + y^3$ is ...
1
vote
2answers
39 views

implicit derivation of this assignment?

I have this old examination assignment, where I have a function for some curve and the coordinates to a point. The subject is to determine the degree of the curve in the given point. The expression ...
0
votes
2answers
46 views

implicit derivates incorperating laplace's equation

If $f(x,y)$ is a harmonic function show that the function $F(x,y)=f(x^2-y^2,2xy)$ is also harmonic. You have to use Laplace's formula to prove this, unless there is an easier way. I'm having trouble ...