Question

Find the derivative and simplify. y = (8x + 7)(x² – 3x).

Answer 1

The derivative is
`y'=24x^2-34x-21`

Explanation:

Given : Equation
`y = (8x+7)(x^2-3x)`

To find : The derivative and simplify ?

Solution :

`y = (8x+7)(x^2-3x)`

First we simply the product,

`y = (8x)(x^2)-(8x)(3x)+7(x^2)+7(-3x)`

`y = 8x^3-24x^2+7x^2-21x`

`y = 8x^3-17x^2-21x`

Derivative w.r.t. x,

`(dy)/(dx) =(d)/(dx)(8x^3-17x^2-21x)`

`y'=24x^2-34x-21`

Therefore, The derivative is
`y'=24x^2-34x-21`