Answer:
The derivative is [tex]y'=24x^2-34x-21[/tex]
Step-by-step explanation:
Given : Equation [tex]y = (8x+7)(x^2-3x)[/tex]
To find : The derivative and simplify ?
Solution :
[tex]y = (8x+7)(x^2-3x)[/tex]
First we simply the product,
[tex]y = (8x)(x^2)-(8x)(3x)+7(x^2)+7(-3x)[/tex]
[tex]y = 8x^3-24x^2+7x^2-21x[/tex]
[tex]y = 8x^3-17x^2-21x[/tex]
Derivative w.r.t. x,
[tex]\frac{dy}{dx} =\frac{d}{dx}(8x^3-17x^2-21x)[/tex]
[tex]y'=24x^2-34x-21[/tex]
Therefore, The derivative is [tex]y'=24x^2-34x-21[/tex]
