Let $\mathrm{f}(x) = a^x$, where $a 0$ and $a \neq 1$. Show that \(\mathrm

Question

Let $\mathrm{f}(x) = a^x$, where $a > 0$ and $a \neq 1$. Show that $\mathrm{f}'(x) = a^x \ln a$ by using differentiation from first principles. Let $\mathrm{g}(x) = \mathrm{e}^x$. Hence, or otherwise, show that $\mathrm{g}'(x) = \mathrm{e}^x$.

Accepted Answer

(i) $f'(x)=a^x\ln a$, from first principles for $a>0$, $a\ne1$. (ii) $g'(x)=e^x$.

Techniques of Differentiation - Differentiation by First Principles

Techniques of Differentiation - Differentiation by First Principles

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