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Nadya [2.5K]
2 years ago
13

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

Mathematics
1 answer:
FromTheMoon [43]2 years ago
3 0

\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}{}  } }}

____________________________________

\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 ❞

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