What Wavelength Maximizes u(lambda) for a 50,000 K Star?

[platonic]

Homework Statement

At what wavelength is u(lambda) a maximum for a star with a surface temperature of 50,000 K?

Homework Equations

Planck's law
u(lambda)=8(pi)hc/(lambda^5*(e^(hc/kTlambda)-1)

The Attempt at a Solution

I think the maximum is where the derivative of the function u(lambda)=0, but the derivative is too messy to solve in terms of lambda so I can't find the wavelength. So I think I'm way off as far as how to solve it. Any help would be appreciated.

 

[Oerg]

well, the differentiation should be done in order to get \lambda at maximum energy density. The differentiation isn't too hard, try using the product rule first.