Let y = x^(a/b) for integers "a" and "b". Raise both sides to the "bth" power and use implicit differentiation to prove the power rule y' = (a/b)x^(a/b-1).
Hello, erimat89!
I'll do it in LaTex . . .
Let for integers
Raise both sides to the power and use implicit differentiation
to prove the power rule: .
We have: . .[1]
Raise to the power: . .[2]
Differentiate implicitly: . .[3]
Divide [2] by
Substitute [1]: .
Substitute into [3]: .