Question

2.1
Find (dy/dx)
if y=root x​

Answer 1

Explanation:

$\bold{y = \sqrt{x} }$

$\bold{y = {x}^{ \frac{1}{2} } }$

Differentiating with respect to x .

$\bold{\frac{dy}{dx} = \frac{d}{dx} ({x}^{ \frac{1}{2} } })$

$\bold{ = \frac{1}{2} {x}^{ \frac{1}{2} - 1 } }$

$\bold{ = \frac{1}{2} {x}^{ \frac{1 - 2}{2} } }$

$\bold{ = \frac{1}{2} {x}^{ \frac{ - 1}{2} } }$

$\bold{ = \frac{1}{2 {x}^{ \frac{1}{2} } } }$

$\bold{ = \frac{1}{2 \sqrt{x} } }$

I hope it is helpful