SOLUTION: Hello friends, I have a question about a derivative. I was asked to find the derivative of y = x(2x+1)^4 I came out with 8x(2x+1)^3 +(2x+1)^4 the book is simplifying it to (2x+1)

Question 957361: Hello friends, I have a question about a derivative. I was asked to find the derivative of y = x(2x+1)^4 I came out with 8x(2x+1)^3 +(2x+1)^4 the book is simplifying it to (2x+1)^3(10x+1) How is this possible? thank you in advance friends !
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the book is very clever.

8x * (2x+1)^3 + (2x+1)^4 is equal to:

8x * (2x+1)^3 + (2x+1)^3 * (2x+1)

factor out the common term and you get:

(2x + 1)^3 * (8x + (2x + 1))

combine like terms and you get:

(2x + 1)^3 * (10x + 1)

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