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Continuity and Differentiability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability2 Marks
Question
Differentiate $a^x$​​​​​​​ w.r.t. x, where a is a positive constant.
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Answer

Let $y = a^x$ . Then
log y = x log a
Differentiating both sides w.r.t. x, we have
$\frac{1}{y} \frac{d y}{d x}$ = log a
or $\frac{d y}{d x}$ = y log a
Thus $\frac{d}{d x}(a^x) = a^x \log a$

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