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

Question

Please SHOW THE WORK!!!

Find DERIVATIVE of the function, using the PRODUCT RULE ONLY!!!!

Answer 1

(fg)' = f'g + fg'
= (4x + 4)(5x^3 + 2x + 2) + (2x^2 + 4x - 3)(15x^2 + 2x)
multiply it out:
(20x^4 + 8x^2 + 8x + 20x^3 + 8x + 8)+(30x^4 + 4x^3 + 60x^3 + 8x^2 - 15x^2 - 6x)
combine like terms:
(20x^4 + 30x^4)+(20x^3 + 4x^3 + 60x^3) + (8x^2 + 8x^2 - 15x2) + (8x + 8x - 6x) + 8
= 50x^4 + 64x^3 + x^2 + 10x + 8
double check my math..

Answer 2

Product rule says that when you have a product of 2 or more functions the derivative will be

F(X) = G(X)*H(X)

F'(x) = G'(x)*H(X) + G(X)*H'(x)

So if

G(X) = 2x^2 + 4x - 3

The derivative is
G'(x) = 4x + 4

If H(x) = 5x^3 + 2x +2

H'(x) = 15x^2 + 2

Plugging everything back into our definition

F'(X) = (4x+4)*(5x^3 + 2x +2) + (2x^2 + 4x - 3)*(15x^2 + 2)

You can then multiply everything out and simplify using algebra.

Answer 3

The product rule states

if f(x) = h(x)*g(x),

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

in your example:

f(x) = (2x^2 + 4x -3)*(5x^3 + 2x + 2)
g(x) = 2x^2 + 4x -3
g'(x) = 4x + 4
h(x) = 5x^3 + 2x + 2
h'(x) = 15x^2 + 2

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

Answer 4

g´(x) =(4x+4)*(5x^3+2x+2)+(2x^2+4x+3)(15x^2+2)
g´(x) =50 x^4+80x^3+57x^2+24x+14