चित्र के आधार पर चारित्रिक विशेषताओं व _______ का वर्णन करना चाहिए
Answers
Explanation:
Let The Given Function be = y
-------------------------------
▪ Given :-
\large \bf{y = {x}^{1/x }}y= x1/x
-------------------------------
▪ To Find :-
\purple{ \bf\large \dfrac{dy}{dx} } dxdy
-------------------------------
▪ Solution :-
We Have ,
\large \mathtt{y = x {}^{1/x} }y=x1/x
\begin{gathered} \large \bigstar \underline{ \pmb{ \mathfrak{ \text{T}a \text king \: \: \text Log \: \: Both \: \: \text Side }}} \\ \end{gathered}★ Taking Log Both Side Taking Log Both Side
\begin{gathered} : \longmapsto \sf \log y = \log { \mathtt x}^{1/ \mathtt x} \\ \\ : \longmapsto \sf \log y = \frac{1}{ \mathtt x} \log \mathtt x \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \{ \because log {m}^{n} = n. log m \}\end{gathered}: ⟼ logy = log x1/x : ⟼logy= x1 logx {∵ logmn =n.logm}
\large\bigstar \underline{ \pmb{ \mathfrak{ Differentiating\:both\: sides\: \text{w.r.t x} }}}★Differentiatingbothsidesw.r.t x Differentiatingbothsidesw.r.t x
\begin{gathered}\small:\longmapsto \sf\frac{1}{y} . \frac{dy}{d \mathtt x} = \frac{1}{ \mathtt x} . \frac{d}{d\mathtt x} ( \log \mathtt x)+ \log \mathtt x. \frac{d}{d\mathtt x} (x {}^{ -1} ) \\ \bf \: \: \: \: \: \: \: \: \: \: \: \: \{ \because Product\:\:Rule \}\\ \\ :\longmapsto \sf \frac{1}{y} . \frac{dy}{d\mathtt x} = \frac{1}{\mathtt x} . \frac{1}{\mathtt x} + \log \mathtt x. \bigg( - \frac{ 1}{ {\mathtt x}^{2} } \bigg ) \\ \\ : \longmapsto \sf \frac{1}{y} . \frac{dy}{d\mathtt x} = \frac{1}{ {\mathtt x}^{2} } - \frac{ \log\mathtt x}{ {\mathtt x}^{2} } \\ \\ : \longmapsto \sf \frac{dy}{d\mathtt x} = y \bigg( \frac{1 - \log\mathtt x}{ {\mathtt x}^{2} } \bigg) \\ \\ \large\purple{ : \longmapsto \pmb{ \underline {\boxed{{ \frac{dy}{dx} = \frac{x {}^{1/x} }{ {x}^{2} } \bigg( 1 - \log x\bigg)} }}}}\end{gathered}:⟼ y1.dxdy = x1.dxd(log x)+ logx.dxd(x−1) {∵ ProductRule} :⟼y1 .dxdy = x1.x1 + logx.(− x2 1 ) :⟼y1.dxdy = x2 1 − x2logx :⟼dxdy =y(x21− logx ) :⟼dxdy = x2 x1/x( 1− logx)dxdy = x2 x1/x( 1− logx)
\begin{gathered} \Large \red{\mathfrak{ \text{W}hich \: \: is \: \: the \: \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}\end{gathered} Which is the required
Answer:
Tara question no jawab.
lakh phata phat
