Derivatives with the PRODUCT RULE?

Question

How do I find the derivative of this? Please show your work in answer, I need to understand it:

g(x) = (2x^2 + 4x - 3) ( 5x^3 + 2x + 2)

Answer 1

Product rule states: f'[x]g[x] + f[x]g'[x]
So take
f[x]= 2x^2 +4x-3
g[x]= 5x^3+2x+2

So f'[x]= 4x+4
g'[x]= 15x^2 +2

Plug that into the product equation:
Answer = (4x+4)(5x^3+2x+2) + (15x^2+2)(2x^2+4x-3)

Answer 2

You can regard g(x) as a combination of f(x) and h(x)

with f(x) = 2x^2+4x-3
and h(x) = 5x^3+2x+2

so g(x) = f(x)*h(x)

now g'(x) = f'(x)h(x) + h'(x)f(x) by the product rule

f'(x) = 4x+4
h'(x)= 15x^2+2

so g'(x) = (4x+4)(5x^3+2x+2)+(15x^2+2)(2x^2+4x-3)

expand that out and simplify.

Answer 3

the rule say this: 2function U and V are factors so (U.V)'= U'.V + U.V'

g(x) = (2x^2+4x-3) (5X^3+2x+2) lets consider g(x) = [f(x)] [h(x)] where f(x) = 2x^2+4x-3 and h(x) = 5x^3+2x+2

so the solution will be:

g'(x) = [f'(x)] [h(x)] + [f(x)] [h'(x)] = (2x^2+4x-3)' (5x^3+2x+2) + (2x^2+4x-3) (5x^3+2x+2)'

by solving this level you get:

g'(x) = (4x+4) (5x^3+2x+2) + (2x^2+4x-3) (15x^2+2) then you will open the parentheses and there's your solution.

Answer 4

g(x) = (2x^2 + 4x - 3) ( 5x^3 + 2x + 2)
g ' (x) = (2x^2 + 4x - 3) ( 15x² + 2) + ( 5x^3 + 2x + 2)(4x + 4)

Answer 5

d(uv) = udv + vdu

let u = 2x^2 + 4x -3

so du = 4x + 4

let v = 5x^3 + 2x + 2

dv = 15x^2 + 2

d[(2x^2 + 4x - 3)(5x^3+2x + 2)

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

=>30x^4 + 60x^3- 45x^2+ x^2+8x -6+20x^4+8x^2+8x+ 20x^3+8x-8

=>50x^4 + 80x^3 -36x^2 + 24x -14

=>2(25x^4 + 40x^3 - 18x^2 + 12x - 7)

Answer 6

I use this phrase that explains the product rule.

1st dee 2nd plus 2nd dee 1st

dee means derivative of...(2nd term or first term)

Here it is spelled out for ya.

(2x^2+4x-3) * (15x^2+2) + (5x^3+2x+2) * (4x+4)
"first" * "dee 2nd" + "2nd" * "dee first"

FOIL those out and ull get your answer.

Answer 7

g(x) = f(x)h(x)

g'(x) = f'(x)h(x) + f(x)h'(x)

The rest is straightforward substitution, then simplification. What aspect of this don't you understand?