Use the Product Rule to find the derivative of the function. Select the correct answer.
$$f ( x ) = ( 4 x + 5 ) \left( x ^ { 2 } - 8 \right)$$
A) $8 x$
B) $2 x + 4$
C) $12 x ^ { 2 } + 10 x - 32$
D) $8 x ^ { 2 } - 40$

Question

Quizplus · Accepted Answer

Using the Product Rule, $f'(x)= (4x+5)(2x)+ (x^2-8)(4)= 8x(4x+5)+4(x^2-8)= 32x^2+40x+4x^2-32= 36x^2+40x-32= 4(9x^2+10x-8)$. Therefore, the correct choice is C.

Use the Product Rule to Find the Derivative of the Function