Question

How do you differentiate `g(x) = (6x+9)(5x^6 - 4)` using the product rule?

Answer 1

`g'(x)=210x^6+270x^5-24`

Explanation:

Given that

`g(x)=(6x+9)(5x^6-4)`

`\frac{d}{dx}g(x)=\frac{d}{dx}(6x+9)(5x^6-4)`

`g'(x)=(6x+9)\frac{d}{dx}(5x^6-4)+(5x^6-4)\frac{d}{dx}(6x+9)`

`g'(x)=(6x+9)(30x^5)+(5x^6-4)(6)`

`g'(x)=210x^6+270x^5-24`