2
votes
4answers
112 views

Confusion about implicit differentiation.

I want to implicitly differentiate $Ax^2 + By^2 + Cxy + Dx + Ey + F = 0$. This is not an exceedingly difficult task, and when I solved it I got $$ y' = -\frac{2Ax + Cy + D}{2By + Cx + E} $$ But my ...
4
votes
2answers
57 views

How can you explain implicit differentiation?

So I am taking calculus 1 online from a local college (bad idea, but the only thing that fit my schedule). The professor used the notation $f'(x) =$ for EVERY function up until two weeks ago. All of ...
1
vote
2answers
32 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 ...
0
votes
2answers
66 views

Differential problem, how to get y''?

I've the following equation: $b^2x^2 + a^2y^2 = a^2b^2$, the first implicit derivative is: $\dfrac{dy}{dx} = \dfrac{-b^2x}{a^2y}$ I do not undertand how to find the second derivative of this ...
0
votes
1answer
24 views

Evaluate derivatives y'(0),z'(0),y''(0),z''(0) of implicit functions y(x) and z(x)

Evaluate derivatives $y'(0)$, $z'(0)$, $y''(0)$ ,$z''(0)$ of implicit functions $y(x)$ and $z(x)$, where $y(0)=-1$ and $z(0)=1$, given by system of equations: $x+y+z=0$ and $x^2+y^2+z^2=0$ First ...
2
votes
0answers
48 views

Help solving this related rates problem.

The question: A car leaves an intersection traveling east. Its position t sec later is given by $x = t^2 + t$ ft. At the same time, another car leaves the same intersection heading north, traveling ...
0
votes
1answer
30 views

I'm having trouble with this question on derivatives.

Carlos is blowing air into a spherical soap bubble at the rate of $7 \mathrm{cm}^3/ \mathrm{sec}$. How fast is the radius of the bubble changing when the radius is $11 \mathrm{cm}$? (Round your answer ...
0
votes
3answers
34 views

Find equation of a line tangent to a curve with a given point

Find equation of a line tangent to the curve at the given point: determine an equation of a line tangent to the curve at the given point: $9(x^2 + y^2)^2 = 100xy^2$; at the point $(1, 3)$ How would ...
0
votes
1answer
30 views

Find the slope of the tangent line to the curve.

So I am trying to find the slope of the tangent line to the curve $$\sqrt{4x+2y} + \sqrt{xy} = \sqrt{38} + \sqrt{24}.$$ at the point $(8,3)$. I ended up implicitly differentiating and getting ...
-1
votes
1answer
50 views

Implicit differentation with chain rule

Problem Find the derivative, using implicit differentiation: $$2x^3=(3xy+1)^2$$ Progress Used the chain rule for the derivative $(3xy+1)^2$. Do I move the $2x^3$ over once I get its ...
-1
votes
4answers
59 views

Second Implicit Derivative [closed]

There is a large argument over the answer to this question: Find the second implicit derivative of $x^2 + xy + y^2=2$. Can someone please answer it and explain their answer?
2
votes
1answer
41 views

Explain the minus sign in the following formula.

I just read that: If $z=f(x,y)=c$, be the equation of a curve, then the slope of the tangent to the curve at any point (x,y), is given by $$m=\frac {dy}{dx}=-\frac{\frac{\partial z}{\partial ...
2
votes
2answers
50 views

Functions that cannot be differentiated in terms of elementary functions

A while ago, I learned how to take the derivative of $y=x^x$ using implicit differentiation, and I wondered if the same trick would work on every function of this type. I tried to differentiate ...
0
votes
2answers
68 views

How to find $\frac{dy}{dx}$ for $\sqrt{xy} = 1$? [closed]

What approach would be ideal in finding $\frac{dy}{dx}$ for $\sqrt{xy} = 1$?
1
vote
2answers
24 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
34 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
41 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
134 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
29 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
1answer
65 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
118 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
39 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
60 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.
-5
votes
2answers
554 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
39 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
93 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
50 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
57 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
317 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
221 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
71 views
-1
votes
2answers
77 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
91 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
338 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
396 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
79 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 $\sec(x)$?
0
votes
1answer
35 views

Question about finding implicit derivatives generally

I have a challenging question for homework. I have done implicit differentiation before in the textbook run-of-the-mill fashion but I do not know how one would go about setting up this an equation for ...
1
vote
2answers
331 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
35 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
157 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
56 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
55 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 ...
-1
votes
5answers
2k views

The rate of change of the distance from the plane to the radar station

Problem statement: A plane flying with constant speed of 4 km/min passes over a ground radar station at an altitude of 6 km and climbs at an angle of 35 degrees. At what rate, in km/min, is the ...
0
votes
1answer
25 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
76 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
103 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
70 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
93 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
41 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.