1. ## Implicit Differentiation

Hi everyone, quick question

Find dy/dx by differentiating implicitly and calculate its value with x=5, y=1

(x^2)-(xy^3)=20

This is what I did:

2x-3xy(dy/dx)=0
-3xy(dy/dx)=-2x
(-2x)/(-3xy)=dy/dx
2xy/3xy=dy/dx
2(5)/3(5)(1)=dy/dx
10/15=dy/dx
2/3=dy/dx

That answer is wrong. Where am I making the mistakes?

Thank you. Much appreciated.

2. Originally Posted by Jea9
Hi everyone, quick question

Find dy/dx by differentiating implicitly and calculate its value with x=5, y=1

(x^2)-(xy^3)=20

This is what I did:

2x-3xy(dy/dx)=0

That answer is wrong. Where am I making the mistakes?

Thank you. Much appreciated.
You made your mistake in the first step, unfortunately. You need to differentiate that as a product rule; you can't just differentiate it as if x were a constant. I'm gonna change things around, so it's a little bit easier. Hopefully this doesn't confuse you...

Differentiating implicitly, you should get $\displaystyle 2x=3y^2xdy+y^3dx$
You're trying to isolate $\displaystyle dy$, so you can rearrange the equation so it reads as follows:
$\displaystyle \frac{2x-y^3}{3xy^2}=dy$

Solve using the point you're given, and you should get $\displaystyle dy=\frac{3}{5}$

Hopefully, that is the answer you were looking for?

3. Thank you!