Question 128713
#1) Multiplying and then differentiating
{{{g(x) = (4x - 3)(2x^2 + 3x + 5)}}}
{{{g(x) = 4x(2x^2 + 3x + 5) - 3(2x^2 + 3x + 5)}}}
{{{g(x) = 8x^3 + 12x^2 + 20x - 6x^2 - 9x - 15}}}
{{{g(x) = 8x^3 + 6x^2 + 11x - 15}}}
{{{dg/dx = 8*3*x^(3-1) + 6*2*x^(2-1) + 11*1*x^(1-1) - 0}}}
{{{dg/dx = 24x^2 + 12x + 11}}}



#2)Product rule
Let {{{g(x) = u(x)v(x)}}} where {{{u(x) = 4x - 3}}} and {{{v(x) = 2x^2 + 3x + 5}}}.
Using Product rule of differentiation
{{{dg/dx = u(x)(dv/dx) + (du/dx)v(x)}}}
{{{dg/dx = (4x - 3)(4x + 3) + 4(2x^2 + 3x + 5)}}}
{{{dg/dx = 16x^2 - 9 + 8x^2 + 12x + 20)}}}
{{{dg/dx = 24x^2 + 12x + 11}}}