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

96x+28

Explanation:

Given function,

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

Differentiating with respect to x,

`(dy)/(dx)=(d)/(dx)[(6x+5)(8x-2)]`

By the product rule of derivatives,

`(dy)/(dx)=(d)/(dx)(6x+5).(8x-2)+(6x+5).(d)/(dx)(8x-2)`

`(dy)/(dx)=6(8x-2)+(6x+5)8`

`(dy)/(dx)=48x-12+48x+40`

`(dy)/(dx)=96x+28`

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