`f(x) = (x^2)(x - 2)^4` Find the derivative of the function.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to use the product and chain rules to evaluate the derivative of the function, such that:

`f'(x) = (x^2)'(x - 2)^4 + (x^2)((x - 2)^4)'`

`f'(x) = (2x)(x - 2)^4 + 4(x^2)((x - 2)^3)*(x-2)'`

Factoring out 2`x(x-2)^3` yields:

`f'(x) = (2x)(x - 2)^3 (x - 2 + 2x)`

`f'(x) = (2x)(x - 2)^3 (3x - 2)`

Hence, evaluating the derivative of the function, using the product rule, yields` f'(x) = (2x)(x - 2)^3 (3x - 2).`