Question

How do you differentiate `g(y) =(x^3 + x)(4x^2+5)` using the product rule?

Answer 1

Product rule states that for `y=f(x)g(x)`, then `y'=f'(x)g(x)+f(x)g'(x)`

Explanation:

`(dy)/(dx)=(3x^2+1)(4x^2+5)+(x^3+x)(8x)`

`(dy)/(dx)=(12x^4+15x^2+4x^2+5)+(8x^4+8x^2)`

`(dy)/(dx)=20x^4+27x^2+5`