Partial Derivatives: Show bz(x)=az(y)

[Lonely Lemon]

Homework Statement

Suppose that z=f(ax+by), where a and b are constants. Show that bz(x) = az(y).

z(x) means partial derivative of z with respect to x, as for z(y).

Homework Equations

The Attempt at a Solution

Say z=ax+by

z(x) = a

z(y) = b

So bz(x) = ba = ab = az(y)

I'm not sure that this is a correct analysis - because I know f(ax+by) doesn't necessarily mean z = ax+by... How should I interpret this problem?

 

[hotvette]

Keep f general and use the chain rule. It might help to let u = ax + by.