Question

$\large{\red{\bf Question }}$

if $\sf y = x^\frac{1}{2}$

find the value of $\sf\dfrac{dy}{dx}$

Class - 11th

Juniors stay away​

Answer 1

$\huge† \huge \bold{\: \pmb {\red{ Answer }} }$

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

$\tt We\:the\:the\:formula$

$\tt\boxed{\bold{\underline{\green{\tt \frac{d({x}^{n})}{dx} = n{x}^{n-1} }}}}$

$\\ \tt \implies \frac{dy}{dx} = \frac{1}{2}{x}^{\frac{1}{2}-1}$

$\tt \implies \frac{dy}{dx} = \frac{1}{2}{x}^{- \frac{1}{2}}$

$\tt \implies \frac{dy}{dx} = \frac{1}{2} \frac{1}{{x}^2}{\frac{1}{2}}$

$\tt \implies \frac{dy}{dx} = \frac{1}{2} \frac{1}{\sqrt{2}} \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt \frac{dy}{dx} = \frac{1}{2\sqrt{x}} }}}}$