Answer
(a) applying the Product Rule: $y'=30x^{2}+14x-12$
(b) multiplying the factors to produce a sum of simpler terms to
differentiate: $y'=30x^{2}+14x-12$
Work Step by Step
$y=(2x+3)(5x^2-4x)$
(a) applying the Product Rule:
$y'=f'(x)⋅g(x)+f(x)⋅g'(x)$
$y'=((1)(2)x^{1-1}+0)(5x^2-4x)+(2x+3)((2)(5)x^{2-1}-(1)(4)x^{1-1})$
$y'=(2)(5x^2-4x)+(2x+3)(10x-4)$
$y'=10x^2-8x+20x^2-8x+30x-12$
$y'=30x^2+14x-12$
(b) multiplying the factors to produce a sum of simpler terms to
differentiate:
$y=(2x+3)(5x^2-4x)$
$y=10x^3-8x^2+15x^2-12x$
$y=10x^3+7x^2-12x$
Derivating the function using the Power Rule
$y'=(3)(10)x^{3-1}+(2)(7)x^{2-1}-(1)(12)x^{1-1}$
$y'=30x^{2}+14x-12$
