1. ## partial derivatives/chain rule?

Im having a little trouble with this question:
Given that z = f(u) where u = x+my and f is an arbitrary function, find the two values of m for which z satisfies the equation
12(d^2z/dx^2) + (d^2z/dxdy) - (d^2z/dy^2) = 0
where all the derivatives are partial derivatives

2. ## Re: partial derivatives/chain rule?

So
$(\dfrac{\partial f}{\partial u}\left(\dfrac{\partial{u}}{\partial{x}}\right))$ and so on so forth. Thats the chain rule. Do you get it?
Then the product rule states $(f(x)g(x)) ' = f'(x)g(x)+f(x)g'(x)$
Use them together i.e. differentiate once and the 2nd time use the product rule also.