Question

explain this , i didnt get it

try

the first who write answer will be marked as brainlist

Answer 1

$\displaystyle{\sf{\frac{d}{dx}(x+\frac{1}{\sqrt{x} } )^2 }}$

$\displaystyle{\sf{By\ power\ rule:-}}$

$\displaystyle{\sf{=2(x+\frac{x}{\sqrt{x} } ).\frac{d}{dx}(x+\frac{1}{\sqrt{x} } ) }}$

$\displaystyle{\sf{This\ differentiation\ is\ linear:-}}$

$\displaystyle{\sf{=2(x+\frac{1}{\sqrt{x} } )\bigg[\frac{d}{dx}(x)+\frac{d}{dx}(\frac{1}{\sqrt{x} } )\bigg]}}$

$\sf{Applying\ power\ rule:-}$

$\displaystyle{\sf{=2(x+\frac{1}{\sqrt{x} })\bigg[1+(-\frac{1}{2})x^{-\frac{1}{2}-1 } \bigg] }}$

$\displaystyle{\sf{=2\bigg(1-\frac{1}{2x^\frac{3}{2} } \bigg)\bigg(x+\frac{1}{\sqrt{x} } \bigg)}}$

$\displaystyle{\sf{By\ simplifying:-}}$

$\boxed{\displaystyle{\sf{=\frac{2x^3+x^\frac{3}{2}-1 }{x^2} }}}$

$\rule{150}2$

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