Well actuallly 2 thms. They have to do with homogeneous functions. f(tx1,...,txn) = t^k * f(x1,...,xn). Now how do you show A) d/dx1 f(tx1,...,txn) = t^k-1 * d/dx1 f(x1,...,xn) and B) kt^(k-1)*f(x1,...,xn) = x1*d/dx1 f(tx1,...,xn) + xn*d/dxn f(x1,...,xn)(adsbygoogle = window.adsbygoogle || []).push({});

A) In the book They say that differentiating the first equation (definition of homogeneous function of degree k) by its first argument yields: d/dx1 f(tx1,...,txn) * t = t^k d/dx1 f(x1,...,xn) from which A easily follows. But how do they get this? I know you have to apply the chain rule somehow but im not sure exactly...

B)Same as A, i end up with expressions like d/d(tx1) x1 which intuitively seems like t but im not sure.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Simple Theorem

**Physics Forums | Science Articles, Homework Help, Discussion**