Prove Power Rule: Implicit Differentiation w/ Rational Exponents

[mattxr250]

Ok guys, I'm new here and I need some help with a math problem...

The problem asks me to prove the power rule ---> d/dx[x^n] = nx^(n-1) for the case in which n is a ratioinal number...

the one stipulation is that I have to prove it using this method: write y=x^(p/q) in the form y^q = x^p and differentiate implicitly...assume that p and q are integers, where q>0.

Thanks for any help

Matt

 

[LeonhardEuler]

Would I be correct in guessing that we are allowed to assume that the power rule holds for integers? If so, then it is simply a matter of differentiating both sides of the equation y^q=x^{p} and then solving for y'. Where are you stuck?

 

[Hurkyl]

Don't multiple post.