how do you find the derivative of ((x^3+1)/x)^5

Question

i need help with deriavtive problems and i need to understand how to do it for a final.

Answer 1

y =( ( x^3 + 1 )/x )^5

dy/dx = 5[ ((x^3 + 1 )/x)^4] * d((x^3 + 1 )/x)

                                                   d(x^3 + 1 )*x - ( x^3 + 1 )*d(x)

dy/dx = 5 ((( X ^3 + 1 )/X)^4) * ------------------------------------------

                                                                               X^2

                                                 3x^2 * x - ( X^3 + 1 )

dy/dx = 5((( x^3+1)/x)^4) * ---------------------------------------

                                                             x^2

                                                      3x^3 - x^3 - 1

dy/dx = 5 ((( x^3 + 1)/x)^4) *  --------------------------------

                                                           x^2

dy/dx =[5(((x^3 + 1 )/x)^4) * ( 2x^3 - 1 )]/x^2