For questions on finding and evaluating derivatives when a function is defined implicitly.
Questions tagged [implicit-differentiation]
1329 questions
7
votes
1 answer
Implicit differentiations of same equation with two different answers:Why?
I've an equation that I like to use for implicit differentiation. The equation is:$x^2 = \frac{(x+2y)}{(x-2y)}$
I used two different methods but got two different answers for same equation.
Can anyone kindly tell me where I am wrong? Why am I…
user35885
5
votes
1 answer
Can every implicit function be written explicitly?
So we were learning implicit differentiation a couple of months ago, and I noticed that while for some equations, like ${{x}\over{y}}=1$ can easily be rewritten as $y=x$ and therefore have a very easy derivative to take, some equations, especially…
scrblnrd3
- 488
4
votes
2 answers
Implicit differentiation for circle
Circle with equation $x^2+y^2-2x-2y+2 = 0$. When we do the implicit differentiation what we get is $\frac{dy}{dx} = \frac{1-x}{1-y}$, but what I noticed is that the radius of this cicle is zero, hence it is a point then what would this…
Vasu Mistry
- 195
3
votes
2 answers
Implicit Second Derivatives using Partial Derivatives
I've got a pretty simple derivative question for you guys. Currently, I'm a high school shop teacher preparing kids for a timed calculus competition. It's been almost 45 years since I've taken multivariate calculus, and I'm having a hard time…
Mike Jones
- 31
3
votes
2 answers
Finding the second derivative of a function (implicit differentiation)
I am not sure if I got the correct answer or not. It was a homework from my textbook, and it does not have answers for even number questions...
Original Function: $x^2y-4x=5$
$\frac{dy}{dx}$ = $\frac{4-2xy}{x^2}$
It seems I got to finding the…
hs2345
- 123
3
votes
1 answer
second derivative of an implicit system of equations
The system of equations:
$x-u^2-v^2+9=0$
$y-u^2+v^2-10=0$
defines $(u,v)$ as a function of $(x,y)$ in every point $u\cdot v\ne 0$
I wish to find $u_{xx}$
I managed to find $u_x$:
if $F=(x-u^2-v^2+9,y-u^2+v^2-10)$ than $u_x=\frac{\partial u}{\partial…
segevp
- 1,015
3
votes
1 answer
Finding a tangent line parallel to the x-axis with dy/dx
$x^2+xy+y^2=7$
Find $dy/dx$
$dy/dx= (-2x-y)/(x+2y)$
How do I take $dy/dx$ and get the equation of the tangent line parallel to the $x$-axis?
Paul
- 31
3
votes
3 answers
Implicit Differentiation: $(x/y)+(y/x) =1$
Hi can anyone please tell me where I goes wrong with this question:
Find $ \frac{dy}{dx} $ for the curves defines by this equation:
\begin{align}
\frac{x}{y} + \frac{y}{x} = 1
\end{align}
Here is what I did:
\begin{align}
&\frac{y-xy'}{y^2}…
Justin HT
- 109
3
votes
2 answers
Second derivative of x^(4) + y^(4) = 16 by implicit differentiation
Find $y''$ if $x^4 + y^4 = 16$ by implicit differentiation
So after the first implicit differentiation I got this equation (let's call it A):
$4x^3 + 4y^3*\frac{dy}{dx} = 0$ Where $\frac{dy}{dx}$ is $y'$
At this point the text book finds the second…
Eric
- 311
2
votes
3 answers
Implicit differentiation help please
So I do not understand the concept at all. Could somebody explain it to me, in very dumbed down terms, using the problem $x^2y + xy^2 = 6$?
All I have down is that it is equal to $4xy + x^2 + y^2 = 6$, and even that could be wrong. Help!
Ethan
- 105
2
votes
2 answers
Help with implicit differentiation simplifications
STEP 1: $$ (x+y)^{3} = x^3 + y^3 $$
STEP 2: $$ 3(x+y)^2 (1+ dy/dx) = 3x^2 + 3y^2(dy/dx) $$
STEP 3: $$ 3(x+y)^2 + \frac{dy}{dx}\cdot3(x+y)^2 = 3x^2 + 3y^2(dy/dx)$$
STEP 4: $$\frac{dy}{dx} \cdot 3(x+y)^2 = 3x^2 + 3y^2(dy/dx) - 3(x+y)^2$$
STEP 5:…
hs2345
- 123
2
votes
1 answer
A problem related to implicit differentiation
This was a homework assignment I had to do a while ago:
The curve K is given by the set of points $(x,y) \in \mathbb{R}^2$ such that $9x + 27y - \frac{10}{81}(x+y)^3 = 0 $. There is also a straight line $l$ tangent to $K$ which goes to $(0,0)$.
The…
Max Muller
- 7,006
2
votes
1 answer
Equation of locus of moving point
How to find the equation of locus of a moving point such that its perpendicular distance from a function $f(x)$ is always $g(x)$?
Tom Lynd
- 1,342
2
votes
0 answers
Find the derivative of $x^{\sqrt{y}}=y^{\sqrt{x}}$.
I am trying to solve:
$x^{\sqrt{y}}=y^{\sqrt{x}}$
Here's my solution. Please correct me if there is an error and kindly explain why.
$\sqrt y\ln{x}=\sqrt…
PRD
- 611
2
votes
1 answer
Why do we call $y$ a function of $x$ in implicit differentiation?
When we have something like $y = 2x$ we understand $y$ to be the value of the function $f$ at each point $x$ where $f(x) = 2x$, to reiterate, $y$ is not a function but merely a label for the output of $f$. In the case of implicit differentiation we…
Nav Bhatthal
- 1,057