Partial Derivatives with trig?

Question

I'm not sure how to solve these two problems. I am required to solve them with respect to X and Y. I am required to find the second derivatives.

z=3sin(x^2y^3)

z/x^2 =

z/y^2 =

I'm not sure where to start on the above questions. Do I figure out the first derivative with the chain rule and then use the product rule to figure out the second derivative?

The second question is:

z=e^(2x)siny

Is this simply 2e^(2x) for the first derivitive and 4e^(2x) for the second? Or is it more complicated then that?

siny throws me off.

I also have to solve the previous question for

z/y^2 (second derivative) =

Why don't math instructors ever ask questions you can find in a text book or online?

Answer 1

simply differentiate twice with respect to each variable.

remember: when differentiating with respect to x, y is a constant so any function containing y does not change. when differentiating wrt y, x is a constant.