Question

what is the derivative of sin(xy), and how?

Answer 1

With respect to x or y?

Answer 2

with both

Answer 3

i am doing implicit differentiation

Answer 4

if\[d/dx[\sin(xy)]\]
Then you will have to do the chain rule getting:
\[[d/dx(xy)][dy/dx(\sin(xy)]\]
For the first part
\[d/dx(xy)=y\]
and second
\[d/dx[\sin(xy)]=cos(xy)\]
So,
\[d/dx[\sin(xy)]=y \sin(xy)\]

differentiating with respect to y will be done the same way with the chain rule, except it will be:
\[d/dy[\sin(xy)]=x \cos(xy)\]