Differentiation - Help for exam prep!

Question

Differentiate the following function and simplify.

 

h(x) = x² · √8-x

 

 

Answer = 2x√8-x - x/2√8-x

 

Could you show me the step by step process and which rules to use in order to differentiate this function?

Answer 1

h(x) = x²√(8-x)

 

By the Product Rule, h'(x) = 2x√(8-x) + ½(8-x)^-½(-1)x²

 

                                      = 2x√(8-x) - x² / [2√(8-x)]

 

                                      = [4x(8-x) - x²] / [2√(8-x)]

 

                                      = (32x - 5x²) / [2√(8-x)]