Question

z=f(xy). Suppose f'(1)=1/3. Find dz/dx at (1/3, 3).

Answer 1

ok so again treat y as a constant:

z=f(xy)
dz/dx = f ' (x*y) * y (chain rule)

Answer 2

now plug in whatever you know to find dz/dx

Answer 3

So dz/dx=f'(xy)*dy/dx?

Answer 4

Ok let me break this down to something a little easier.
Suppose you have f(x) = Sin(x*9)

Answer 5

So z = Sin(x*9)
dz/dx would then be Cos(x*9) * d(x*9)/dx = Cos(x*9) * 9

Answer 6

In our case
z = f(x*y)
dz/dx = { d[ f(x*y) ]/dx } * d [ x*y ] /dx