Question

differnetiate using chain rule:- √sin√x​

Answer 1

Answer:

$\large\boxed{\sf{\dfrac{ \cot( \sqrt{x} ) }{4 \sqrt{x} }}}$

Step-by-step explanation:

$y = \sqrt{ \sin( \sqrt{x} ) }$

Let's assume,

$t = \sqrt{x }$

Differentiating both sides,

$= > \frac{dt}{dx} = \frac{1}{2 \sqrt{x} }$

Also, let's assume,

$u = \sin( \sqrt{x} ) \\ \\ = > u = \sin(t)$

Differentiating both sides,

$= > \frac{du}{dt} = \cos(t)$

Therefore, we have,

$y = \sqrt{u}$

Differentiating both sides,

$= > \frac{dy}{du} = \frac{1}{2 \sqrt{u} }$

Therefore, we have,

$= > \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dt} \times \frac{dt}{dx} \\ \\ = > \frac{dy}{dx} = \frac{1}{2 \sqrt{u} } \times \cos(t) \times \frac{1}{2 \sqrt{x} } \\ \\ = > \frac{dy}{dx} = \frac{ \cos(t) }{4 \sqrt{ux} } \\ \\ = > \frac{dy}{dx} = \frac{ \cos( \sqrt{x} ) }{4 \sqrt{x} \sin( \sqrt{x} ) } \\ \\ = > \frac{dy}{dx} = \frac{ \cot( \sqrt{x} ) }{4 \sqrt{x} }$

Answer 2

Answer:

4 square root of x

Step-by-step explanation: