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

1 Answer

g' (x)=d/dxg(x)=50x^4+80x^3-33x^2+24x+2

Explanation:

For derivative of product , we have the formula
d/dx(uv)=u dv/dx + v du/dx

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

We let u=2x^2+4x-3 and v=5x^3+2x+2

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

d/dx(g(x))=(2x^2+4x-3) (15x^2+2)+(5x^3+2x+2) (4x+4)

Expand to simplify

d/dx(g(x))=(2x^2+4x-3) (15x^2+2)+(5x^3+2x+2) (4x+4)

d/dx(g(x))=30x^4+4x^2+60x^3+8x-45x^2-6+20x^4+20x^3+8x^2+8x+8x+8

Combine like terms

d/dx(g(x))=50x^4+80x^3-33x^2+24x+2

God bless...I hope the explanation is useful.