For questions on finding and evaluating derivatives when a function is defined implicitly.
Questions tagged [implicit-differentiation]
1329 questions
1
vote
1 answer
Differentiation of an implicit function
$$ x = y^x $$
been working through some implicit functions and this has me a bit, I don't think my answer is correct
I have treated $y$ as $y(x)^x$ and differentiated with respect to x
joe
- 107
1
vote
1 answer
Solving $x^2 (x-y)^2 = x^2 - y^2$ using implicit differentiation
I have a test tomorrow and I am doing homework to review and study. The problem is to differentiate
$$
x^2 (x-y)^2 = x^2 - y^2.
$$
I tried multiple times; however, every time I try I get the incorrect answer. It would be greatly appreciated if…
user225022
- 45
1
vote
1 answer
Vertical Tangent line with Implicit Differentiation
The original equation is $$x^2-2xy+y^3= 4$$ and I hope the derivative to be $$\frac{dy}{dx} = \frac{2(x-y)}{2x-3y^2}$$
I know the vertical tangent is when the denominator is $0$, but I am having trouble determining the vertical tangent.
Jocelyn
- 11
1
vote
4 answers
Take the derivative of another variable
How can you take the derivative
$$\frac{d}{dx}(y^2)$$
I don't understand how the chain rule applies here. Someone told me that the chain rule applies here because $y$ can be expressed in some type of $x$ expression, but I still don't get it.
So, I…
user1534664
- 1,272
0
votes
1 answer
Implicit Differentiation - Can't spot my error
I can't figure out where I went wrong in finding the derivative for this function. Can anyone spot my error?
$2(x^2 + y^2)^2 = 25(x^2 - y^2)$
$4(x^2 + y^2)(2x + 2yy') = 25(2x - 2yy')$
$\displaystyle \frac{2x + 2yy'}{2x - 2yy'} = \frac{25}{4(x^2 +…
akuryo
- 53
0
votes
3 answers
Find $dy/dx$ where $(7x+2y)^2=6x^4y^3$
Find $\displaystyle\frac{\mathrm{d}y}{\mathrm{d}x}$ where
$$(7x+2y)^2=6x^4y^3$$
This is on my homework but book has different examples so I don't know what side to start on.
0
votes
1 answer
Solving for the rate at which water is pumped into a conical tank using related rates.
Water is leaking out of an inverted conical tank at a rate of $12000.0$ cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height $8.0$ meters and the diameter at the top is $3.5$…
jrounsav
- 139
0
votes
1 answer
Implicit differentiation and tangents
is the question.
I started doing it then got stuck so I looked at the mark scheme:
Now, I don't understand the
$-sin(-2\pi)(x\frac{dy}{dx}+y)=0$ bit
$(x\frac{dy}{dx}+y)=0$
Solving $\frac{dy}{dx}=0$,…
Jim
- 1,210
0
votes
1 answer
Implicit differentiation
Question: Find the gradient of the curve $x \ln y - \frac{x}{y}=2$ at $(-1,1)$
I've done something wrong as I got the gradient to be $0$ when the answer in the back says $-0.5$
Can someone help me with this question?
edit:
I…
Jim
- 1,210
0
votes
1 answer
Implicit Derivative
I did lots of calculation, but it just only going to be nothing but mess. If anyone could help me, thanks.
Jakoer
- 315
0
votes
3 answers
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 know how to solve implicit differentiates in…
rablentain
- 645
0
votes
1 answer
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 right away- is this way wrong? especially the second…
chrissy kwon
- 81
0
votes
1 answer
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:
First take derivative w.r.t $y$ and I get $1 =…
user123818
- 69
0
votes
2 answers
Implicit function problem
maybe I'm just blind but I cannot see what to do here:
$$F(x_1+x_2+x_3,x_1^2+x_2^2+x_3^2)=0$$
$$x_3=f(x_1,x_2)$$
I would like to obtain the differential of $f$ in terms of the partial derivatives of $F$.
This screams implicit function theorem, but,…
Felix H
- 35
0
votes
1 answer
Moving expressions around gives different implicit differentiation
Here's an exercise from Thomas Calculus, I need to do an implicit differentiation:
$$
x^3=\frac{2x-y}{x+3y}
$$
If I enter this in Wolfram Alpha, I get:
$$
y'(x) =-\frac{3 x^4 + 18 x^3 y + 27 x^2 y^2 - 7 y}{7 x}
$$
But if I move things around first…
Stanislav Bashkyrtsev
- 589
- 3
- 11