How do you differentiate y=x²(2x+5)³?

1 Answer
Jan 7, 2016

Product rule states that for y=f(x)g(x), then (dy)/(dx)=f'(x)g(x)+f(x)g'(x)

Explanation:

In this case, we'll also need the chain rule to differentiate the second term.

Chain rule: (dy)/(dx)=(dy)/(du)(du)/(dx)

(dy)/(dx)=2x(2x+5)^3+x^2(3(2x+5)^2(2))

(dy)/(dx)=2x(2x+5)^2((2x+5)+3x)