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

1 Answer

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.