Question

dy/dx of x(x^2 - x -2)​

Answer 1

Step-by-step explanation:

Let

$y = x( {x}^{2} - x - 2) \\ \\ \\ = {x}^{3} - {x}^{2} - 2x \\ \\ \\ \frac{dy}{dx} = \frac{d( {x}^{3} - {x}^{2} - 2x)}{dx} \\ \\ \\ = 3 {x}^{2} - 2x - 2 \\ \\ \\ formula \: used \: \\ \\ \\ \frac{d {x}^{n} }{dx} = n {x}^{n - 1}$

THANKS!!!

Answer 2

$\huge \red{ \mathfrak{solution}}$

To find :

$\boxed { \bold{\frac{dy}{dx} = x( {x}^{2} - x - 2)}}$

Here we use the formula :

$\huge \boxed{ \green{\bold{\frac{d}{dx} {x}^{n} = n {x}^{n - 1} }}}$

Solution:

$\leadsto \: \frac{d}{dx} ( {x}^{3} - {x}^{2} - 2x) \\ \\ \leadsto \: \frac{d}{dx} ( {x}^{3} ) - \frac{d}{dx}( {x}^{2} ) - \frac{d}{dx} (2x) \\ \\ \leadsto \: 3 {x}^{2} - 2x - 2$