Question

Find the derivative of the function by using the product rule. Do not find the product before finding the derivative. yequalsleft parenthesis 6 x plus 5 right parenthesis left parenthesis 8 x minus 2 right parenthesis StartFraction

Answer 1

Answer:

96x+28

Step-by-step explanation:

Given function,

$y=(6x+5)(8x-2)$

Differentiating with respect to x,

$\frac{dy}{dx}=\frac{d}{dx}[(6x+5)(8x-2)]$

By the product rule of derivatives,

$\frac{dy}{dx}=\frac{d}{dx}(6x+5).(8x-2)+(6x+5).\frac{d}{dx}(8x-2)$

$\frac{dy}{dx}=6(8x-2)+(6x+5)8$

$\frac{dy}{dx}=48x-12+48x+40$

$\frac{dy}{dx}=96x+28$

Hence, the derivative of the given function is 96x+28.