Question

How do you differentiate `y=x²(2x+5)³`?

Answer 1

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)`