Question

Find the derivative of y = x^3/2.

Answer 1

$\quad \huge \quad \quad \boxed{ \tt \:Answer }$

$\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )= \dfrac{3}{2} \sqrt{x}$

$\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)= \cfrac{- 3}{ {x}^{4} }$

$\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)= \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }}$

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$\large \tt Solution \: :$

properties to be used here :

$\qquad \tt \rightarrow \:\cfrac{d}{dx}( {x}^{ n } ) = n \sdot{x}^{n - 1}$

$\large \textsf{Question : 1}$

$\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )$

$\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3}{2} - 1 }$

$\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3 - 2}{2} }$

$\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{1}{2} }$

$\qquad \tt \rightarrow \:y = \dfrac{3}{2} \sqrt{x}$

$\large \textsf{Question : 2}$

$\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)$

$\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - 3} } )$

$\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 3 - 1} }$

$\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 4} }$

$\qquad \tt \rightarrow \:y = \cfrac{- 3}{ {x}^{4} }$

$\large \textsf{Question : 3}$

$\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)$

$\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{{x}^{ \frac{1}{2} } } \bigg)$

$\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - \frac{1}{2} } } )$

$\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ - \frac{1}{2} - 1} }$

$\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 1 - 2}{2} } }$

$\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 3}{2} } }$

$\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2{x}^{ \frac{ 3}{2} } }$

$\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }}$

Answered by : ❝ AǫᴜᴀWɪᴢ ❞