Question

How do you differentiate `f(x) = (x^2 + 6) (4x^6 + 5)` using the product rule?

Answer 1

`d/dx(x^2+6)(4x^6+5)=24x^5(x^2+6)+2x(4x^6+5)`

Explanation:

According to the product rule,
`d/dx [f(x)*g(x)]=f(x)*g'(x)+g(x)*f'(x)`

`therefored/dx(x^2+6)(4x^6+5)=(x^2+6)(24x^5)+(4x^6+5)(2x)`