Question

Use product rule to calculate the derivative of: 3" title=" {x}^{2} " alt=" {x}^{2} " align="absmiddle" class="latex-formula">
.(2x-1)​

Answer 1

Answer:

18x² - 6x

Step-by-step explanation:

Differentiate using the product rule, that is

y = f(x)g(x), then

$\frac{dy}{dx}$ = f(x)g'(x) + g(x)f'(x)

here

f(x) = 3x² ⇒ f'(x) = 6x

g(x) = 2x - 1 ⇒ g'(x) = 2, thus

$\frac{d}{dx}$(3x²(2x - 1)

= 3x² × 2 + 6x(2x - 1)

= 6x² + 12x² - 6x

= 18x² - 6x