Question

What is the derivative of `(x^3 + 2)^2(x^5 + 4)^4`?

Answer 1

`f^'(x) =2 x^2(x^3+2)(x^5+4)^3 ( 13 x ^5+20 x^2+12)`

Explanation:

`f(x) = (x^3+2)^2 (x^5+4)^4`

Product rule : `d/d x (f g)= f g^'+g f^'`

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

`f^'(x) =2 x^2(x^3+2)(x^5+4)^3 {( 10 x^5+20x^2)+(3 x^5+12)}`

`f^'(x) =2 x^2(x^3+2)(x^5+4)^3 ( 13 x ^5+20 x^2+12)` [Ans]