Question

Use product rule to calculate the derivative of: 3

`{x}^(2)`
.(2x-1)​

Answer 1

18x² - 6x

Explanation:

Differentiate using the product rule, that is

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

`(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

`(d)/(dx)`(3x²(2x - 1)

= 3x² × 2 + 6x(2x - 1)

= 6x² + 12x² - 6x

= 18x² - 6x