For questions on finding and evaluating derivatives when a function is defined implicitly.
Questions tagged [implicit-differentiation]
1329 questions
2
votes
1 answer
First-order non-linear differential equation
I have this equation:
$$x(dx-dy) + y(dx+dy) = 0 $$
I tried to solve it by turning it to fraction-type:
$$\frac{dy}{dx} = \frac{x+y}{x-y}$$
However, I realized that it's not homogeneous, and now I am stuck.
Please help!
Samuel
- 121
2
votes
2 answers
Implicit differentiation
I am currently working on a question which involves me differentiating $$\frac{y}{x}$$
I can't find nothing in books or on the internet about how to deal with this kind of implicit differentiation.
pat
- 21
2
votes
1 answer
Further differentiation
The question tells us that the functions $x(t)$ and $y(t)$ satisfy $dx/dt=-x^2y$ and $dy/dt= -xy^2$ when $t=0$, $x=1$, and $y=2$. I have already worked out that $dy/dx= (xy^2)/(x^2y)$ and that $y=2x$. Now given that $dx/dt=-2x^3$ deduce a formula…
Christie
- 147
1
vote
1 answer
Implicit Diff. check
I have the expression ${\dfrac{x^2+y^2}{x+y}}=3$ and I wanna find $dy/dx$. Here's my approach:
$x^2+y^2=3x+3y$
$\implies (x^2-3x)+(y^2-3y)=0$
$\implies (2x-3)+\dfrac{dy}{dx}(2y-3)=0$
${\implies \dfrac{dy}{dx}=\dfrac{3-2x}{2y-3}}$
Wolfram Alpha gives…
clueless
- 51
1
vote
1 answer
Finding the second derivative by implicit differentiation
Find $y''=y''(x)$ for the function defined by equation $xy+y^2=2x$
I got the first derivative just fine, $y'(x)= \frac{2-y(x)}{x+2y(x)}$ but I'm having trouble with finding the second derivative. After differentiating again and inserting the first…
havukalle
- 21
1
vote
1 answer
Implicit Function Theorem Applied
I am concerened I may have oversimplified my solution to this question.
My solution:
Let $F(x,y,z)=x-e^y\sin(z)$
By the implicit function theorem: $\displaystyle\frac{\partial z}{\partial x}=-\displaystyle\frac{\frac{\partial F}{\partial…
usainlightning
- 1,217
1
vote
2 answers
Implicit differentiation of $x2^y=\ln y$
A curve has implicit equation $x2^y=\ln y$. Find an expression for $\frac{dy}{dx}$ in terms of $x$ and $y$.
I got
$$x 2^y \ln 2 \frac{dy}{dx}+2^y=\frac{1}{y}$$
$$\frac{dy}{dx}=\frac{\frac{1}{y}-2^y}{x \ln 2 \cdot 2^y}$$
which isn't the answer. Can…
Jim
- 1,210
1
vote
2 answers
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 of the curve is: $$ x^2 \sin{\sqrt{y}}+ye^{-2x}=1…
rablentain
- 645
1
vote
1 answer
Finding horizontal tangent line using implicit differentation
How do you find the horizontal tangent line from an equation like this: $x^2 +xy +y^2=6$? I've already found the derivative using implicit differentiation and tried solving for 0...but I have two variables.
1
vote
1 answer
Having trouble finding downward acceleration of top of ladder in a standard, but tricky, ladder and wall problem
An 18-foot ladder extends over a 12-foot wall; the bottom of the ladder is pulled away from the wall at 2'/sec; find the vertical velocity (then acceleration) of the top of ladder when the angle the bottom of the ladder makes with the floor = pi/3…
Victor Jaroslaw
- 139
1
vote
1 answer
A differentiation and double differential function proof
This is a question which I received from my friend as he was not able to solve it. Even I and my professor too failed to solve this question. Pls someone help me with this question.
I have been able to proved it till here-
g(0) 9
user877930
1
vote
1 answer
In the following procedure, how is the function (implicitly) chosen?
Given $x^3+y^3-3xy=0$ we differentiate with respect to $x$ on both sides, yielding $3x^2+3y^2\frac{dy}{dx} -3x\frac{dy}{dx} - 3y = 0$, and rearrange to get
$$
\frac{dy}{dx} = \frac{y-x^2}{y^2-x},\quad y^2\neq x
$$
The original relation…
Peatherfed
- 726
1
vote
2 answers
implicit differentiation
An equation is defined as $x+y+x^5-y^5=0$.
$a$. Show that the equation determines $y$ as a function of $x$ in a neighbourhood of the origin $(0,0)$.
$b$. Denote the function from $(a)$ by $y=\varphi(x)$. Find $\varphi^{(5)}(0)$ and…
user77440
- 73
1
vote
1 answer
how do I differentiate this function implicitly
How do I differentiate $$\frac{(x^2 - 4y^2)} {(x^2 + xy^2)} = 2$$ implicitly? I did it by bringing the denominator over to the other side, and I got $$\frac{-(2x + 2y^2)}{(4xy + 8y)}$$
Here are the images of the question and the suggested answer.
tangolin
- 161
1
vote
1 answer
Proof for derivative of implicit functions
My book says the following:
$f'(x,y)=-\left(\frac{\frac{\partial f(x,y)}{\partial x}}{\frac{\partial f(x,y)}{\partial x}}\right)$
We can use this for differentiating implicit functions($f(x,y)=0$)
However they have not mentioned a proof, which I…
DatBoi
- 4,055