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Continuity and Differentiability — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSContinuity and Differentiability2 Marks
Question
Differentiate $a^x w.r.t. x,$ where a is a positive constant.
✓

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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