# Math Help - Implicit Differentiation w/ sin(x)

1. ## Implicit Differentiation w/ sin(x)

Hey, so I'm having trouble differentiating this problem.....

ysin[x(squared)]=xsin[y(squared)]

any help would be appreciated

2. Originally Posted by CALsunshine
Hey, so I'm having trouble differentiating this problem.....

ysin[x(squared)]=xsin[y(squared)]

any help would be appreciated
$y\sin\left(x^2\right)=x\sin\left(y^2\right)$

You would need to apply product and chain rules when differentiating both sides!

$\frac{d}{\,dx}\left[y\sin\left(x^2\right)\right]=\frac{d}{\,dx}\left[x\sin\left(y^2\right)\right]$ $\implies 2xy\cos\left(x^2\right)+\sin\left(x^2\right)\frac{ \,dy}{\,dx}=\sin\left(y^2\right)+2xy\cos\left(y^2\ right)\frac{\,dy}{\,dx}$

Can you take it from here and solve for $\frac{\,dy}{\,dx}$?

--Chris

3. yes...I can solve for dy/dx from there, thank you so much.