Differentiate the following functions w.r.t.x. : x x - Vidyadip

Question

Differentiate the following functions w.r.t.x. : $\mathrm{x} \sqrt{\mathrm{x}}$

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Answer

$
\begin{aligned}
& \text { Let } \mathrm{y}=\mathrm{x} \sqrt{\mathrm{x}} \\
& \therefore \mathrm{y}=x^{\frac{3}{2}}
\end{aligned}
$
Differentiating w.r.t. $x$, we get
$
\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\mathrm{d}}{\mathrm{d} x} x^{\frac{3}{2}}=\frac{3}{2} x^{\frac{1}{2}}
$

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