Question

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

Answer 1

`(4x+4)(5x^3+2x+2)+(15x^2+2)(2x^2+4x-3)`

`50x^4+80x^3-33x^2+24x+2`

Explanation:

First the product rule is, `g(x)=fprime(x)h(x)+hprime(x)f(x)`

Where `f(x)=2x^2+4x-3`
And `h(x)=5x^3+2x+2`

Now take the derivative of both, this gives you...
`fprime(x)=(4x+4)`
`hprime(x)=(15x^2+2)`

So now plug into the product rule formula
`(4x+4)(5x^3+2x+2)+(15x^2+2)(2x^2+4x-3)`

After multiplying and adding like terms you get
`50x^4+80x^3-33x^2+24x+2`