Question

How do you use the product rule to differentiate `y = (x^2 + 2) (x^3 + 4)`?

Answer 1

If we consider the definition of product rule for the function `y = f(x)*g(x)`, we have `(dy)/(dx) = f'(x)g(x) + f(x)g'(x)`.

Applying such concept to your function, we have

`y = 2x(x^3+4)+(x^2+2)3x^2`

Simplifying:

`y = 2x^4+8x+3x^4+6x^2`

`y=5x^4+6x^2+8x`