Question

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

Answer 1

`8x(3x-5)+3(4x^2+5)`
`36x^2-40x+15`

Explanation:

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

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

Now take the derivative of both, this gives you...
`gprime(x)=(8x)`
`hprime(x)=(3)`

So now plug into the product rule formula
`(8x)(3x-5)+(3)(4x^2+5)`

After multiplying you get
`24x^2-40x+12x^2+15`

You then combine like terms and get the answer which is
`36x^2-40x+15`