How do you differentiate g(x) = (2x^2 + 4x - 3) ( 5x^3 + 2x + 2)g(x)=(2x2+4x3)(5x3+2x+2) using the product rule?

1 Answer
Mar 14, 2018

(4x+4)(5x^3+2x+2)+(15x^2+2)(2x^2+4x-3)(4x+4)(5x3+2x+2)+(15x2+2)(2x2+4x3)

50x^4+80x^3-33x^2+24x+250x4+80x333x2+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