Question

What are the first and second derivatives of y= x-3x^(1/3)

Answer 1

this is just a simple power rule:

y = x^1 - 3x^(1/3)

y' = 1*x^0 - 3*(1/3)x^(1/3 - 1)
= 1 - x^(-2/3)

y'' = 0 - (-2/3)x^(-2/3 - 1)
= 2/3 x^(-5/3)