Question

Find dy/dx if y = sin (x2) ​

Answer 1

Answer:

$y = sin( {x}^{2} )$

Differentiate both sides of the equation.

$\frac{d}{dx} (y) = \frac{d}{dx}( sin( {x}^{2} ))$

The derivative of y with respect to x is y'

Differentiate the right side of the equation,we will get,

$2x \: cos( {x}^{2} )$

Reform the equation by setting the left side equal to the right side.

y'= 2x cos x^2

Replace y' with

$\frac{dy}{dx}$

$\frac{dy}{dx} = 2x \: cos ( {x}^{2} )$