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

1 Answer
Mar 15, 2018

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