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Questions  >>  CBSE XII  >>  Math  >>  Differential Equations
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Q)

Differentiate $a^x$ w.r.t x, where a is a constant


$(A)\;a \;log\; x$
$(B)\;a \;log\; a^x$
$ (C)\;a^x\; log \;a$
$(D)\;x \;log \;a^x$

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A)
Let $y = a^x$
take log on both sides
$\text{log y} = \text{x log a }$
differentiate w.r.t x
$\begin{align*}\frac{1}{y}.\frac{dy}{dx} & = \text{log a} \\ \implies \frac{dy}{dx} & = \text{y log a} \\ & = a^x\text{log a} \end{align*} $
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