Question

How do I find a partial derivative of something like sin(4xy)?

Answer 1

Derivative with respect to what?

Answer 2

pretend one variable is a constant.

Answer 3

both x and y

Answer 4

so for example if you want partial wrt x treat y as a constant

Answer 5

you would get
\[\cos(4xy)\times 4y\]

Answer 6

Oh, partials:

\[\frac{\delta f}{\delta x} = 4ycos(4xy)\]
\[\frac{\delta f}{\delta y} = 4xcos(4xy)\]

Answer 7

Thanks, I didnt know if the chain rule was still in effect.

Answer 8

Certainly is.

Answer 9

You treat the variables you aren't taking the partial with respect to as constant applying all the chain rule stuff, etc.