Asked by david

What is the derivative of the fifth root of x^3?
Answered by Reiny
if y = (x^3)^(1/5)
= x^(3/5)

we would have dy/dx = (3/5)x^(3/5 - 1) = (3/5) x^(-2/5)
Answered by R_scott
fifth root of x^3 = x(3/5)

derivative x^(3/5) = 3/5 x^(-2/5) = 3/5 *[5th root (x^-2)]
Answered by david
Thanks, i get it now
Answered by oobleck
y = (x^3)^(1/5)
Using the chain rule,
y' = 1/5 (x^3)(-4/5) * 3x^2 = 3/5 x^(-12/5 + 2) = 3/5 x^(-2/5)
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