calculate the derivative

Question

^{(x^1/3-x)/x^1/2}

Answer 1

Simplify first:  y = (x^1/3 - x) / x^1/2

 

                        = x^1/3 / x^1/2 - x / x^1/2

 

                        = x^-1/6 - x^1/2

 

So, y' = (-1/6)x^-7/6 - (1/2)x^-1/2