Question

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

Answer 1

`dy/dx = 4x(x^2 + 3)`

Explanation:

`dy/dx (f(x) . g(x)) = f(x) g'(x) + f'(x) g(x)` (Product Rule)

In this example: `f(x) = x^2` and `g(x) = (x^2 + 6)`

Hence:
`dy/dx = x^2 . (2x + 0) + 2x . (x^2 +6)`
`dy/dx = 2x^3 + 2x^3 + 12x`
`dy/dy = 4x(x^2 + 3)`