y^b=x^a
b*y^(b-1)*y'=a*x^(a-1)
y'={a*x^(a-1)}/{b*y^(b-1)}
y'=(a/b)*x^(a-1)/x^(a*(b-1)/b)
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]: .