Question

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

Im not sure I am doing this correctly. I started off using the product rule and got
(x^2+x+1)^5 d/dx(2x-3)^4 + (2x-3)^4 d/dx(x^2+x+1)^5

I then used the chain rule on the d/dx terms leaving me with
(x^2+x+1)^5 4(2x-3)^3 *2 + (2x-3)^4 5(x^2+x+1)^4 *2x+1

I seem to be far off from the answer. The answer in the book is
(2x-3)^3 (x^2+x+1)^4 (28x^2-12x-7)

I have no clue how to get that answer. Help would be GREATLY APPRECIATED!
Thanks

Answer 1

You have to start with the product rule then use the chain rule as you have derivatives of composite functions.

Answer 2

\[\frac{ d }{ dx }(x^2+x+1)^5 = 5(x^2+x+1)^4.(2x + 1)\]