# Prove the Power Rule

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

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LeonhardEuler
Gold Member
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
Staff Emeritus