Question

How do you differentiate `g(y) =(x^2 + 6)(x^2 - 1)` using the product rule?

Answer 1

`2x(2x^2 +5)`

Explanation:

The product rule states that if `h(x) = f(x)g(x)` then `h'(x)= f'(x)g(x) + f(x)g'(x)`
`:. d/dxg(y) =( d/dx(x^2+6))(x^2-1) + (x^2+6)d/dx(x^2-1)`
`= 2x(x^2-1) +(x^2+6)*2x`
`=2x^3 -2x +2x^3 +12x`
`=4x^3 +10x`
`=2x(2x^2 +5)`