Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDifferentiation2 Marks
Question
If $y =\frac{ e ^x}{\sqrt{x}}$, find $\frac{d y}{d x}$ when $x =1$
✓
Answer
$ y=\frac{ e ^x}{\sqrt{x}} $ Differentiating w.r.t. $x$, we get $ \begin{aligned} \frac{ d y}{ d x} & =\frac{ d }{ d x}\left(\frac{ e ^x}{\sqrt{x}}\right) \\ & =\frac{\sqrt{x} \frac{ d }{ d x} e ^x- e ^x \frac{ d }{ d x} \sqrt{x}}{(\sqrt{x})^2} \\ & =\frac{\sqrt{x} e ^x- e ^x \frac{1}{2 \sqrt{x}}}{x} \\ \frac{ d y}{ d x} & =\frac{2 x \cdot e ^x- e ^x}{2 \sqrt{x} x} \end{aligned} $ When $x=1$, $ \frac{ d y}{ d x}=\frac{2(1) e ^1- e ^{ l }}{2 \sqrt{1} .1}=\frac{2 e - e }{2}=\frac{ e }{2} $
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