Question

y=4x/6-2x^2 ,find dy/dx​

Answer 1

Step-by-step explanation:

$y = \frac{4x}{6} - 2 {x}^{2}$

Differentiate wrt x :

$\frac{dy}{dx} = \frac{d}{dx} ( \frac{4x}{6} - 2 {x}^{2} )$

use division rule to differentiate

4x /6

Division rule

if y = u / v then,

dy /dx = (v. du/dx - u. dv/dx)/v²

$= \frac{((6 \times 4) - 4x(0))}{ {6}^{2} } \times 4x \times 1$

$= \frac{24}{36} \times 4x$

$= \frac{24x}{9}$

$= \frac{8x}{3}$

$\frac{dy}{dx} = \frac{8x}{3}$