What is the derivative of the fifth root of x^3?

Answer 1

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)

Answer 2

fifth root of x^3 = x(3/5)

derivative x^(3/5) = 3/5 x^(-2/5) = 3/5 *[5th root (x^-2)]

Answer 3

Thanks, i get it now

Answer 4

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)