`f(x) = (2x - 3)^4 (x^2 + x + 1)^5` Find the derivative of the function.

Expert Answers
gsenviro eNotes educator| Certified Educator

Using the product rule:

`d/dx[a(x)b(x)] = a'(x)b(x) + a(x)b'(x)`  

we get:

`f'(x) = 4(2x-3)^3*(2)(x^2+x+1)^5 `

`+ (2x-3)^4 * 5(x^2+x+1)^4 *(2x+1)`

`= (2x-3)^3 (x^2+x+1)^4 [8(x^2+x+1) + 5(2x+1)(2x-3)]`

`= (2x-3)^3 (x^2+x+1)^4 (28x^2-12x-7)`

Hope this helps.