The derivative of p(x) with respect to x?

Question

Hi.

I would like to find out the answer to this question

I would like to know

the derivative of p(x) with respect to x where

p(x) = ( 5*x^3+5 *x+5 ) ( 3*x^2+2 *x-2 )

so what is p' (x) =

Thanks for any help received. It is very much appreciated.

Answer 1

first you need to multiply out p(x), then it will very easy to derivate with respect to x

p(x) = (5x^3 + 5x + 5) * (3x^2 + 2x -2)

= 15x^5 + 15x^3 + 15x^2 + 10x^4 + 10x^2 + 10x - 10x^3 - 10x - 10

= 15x^5 + 10x^4 + 5x^3 + 25x^2 - 10

you see now it's easy to derivate p(x)

p'(x) = 15*5x^4 + 10*4x^3 + 5*3x^2 + 25*2x - 0

p'(x) = 75x^4 + 40x^3 + 15x^2 + 50x

p'(x) = 5 * (15x^4 + 8x^3 + 3x^2 + 10x)

Answer 2

I'm not simplifying this but its just the product rule.  Derivative of the first times the second plus derivative of second times the first.

(15x^2 +5)(3x^2 +2x -2) + (6x +2)(5x^3 +5x +5)

Answer 3

p(x) = (5x^3 + 5x + 5)(3x^2 + 2x - 2)

using the product rule, we get:

p'(x) = (5x^3 + 5x + 5)*(6x + 2) + (3x^2 + 2x - 2)*(15x^2 + 5)

       = 30x^4 + 10x^3 + 30x^2 + 10x + 30x + 10 + 45x^4 + 15x^2 + 30x^3 + 10x - 30x^2 - 10

      = 75x^4 + 40x^3 + 15x^2 + 50x .