Differentiate a^{x} with respect to x,where a | vedclass

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(A) Let $y = a^{x}$.Taking the natural logarithm on both sides,we get:$\log y = x \log a$Differentiating both sides with respect to $x$,we have:$\frac

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$a^{x} \log a$

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(A) Let $y = a^{x}$.Taking the natural logarithm on both sides,we get:$\log y = x \log a$Differentiating both sides with respect to $x$,we have:$\frac{1}{y} \frac{dy}{dx} = \log a$Multiplying both sides by $y$,we get:$\frac{dy}{dx} = y \log a$Substituting $y = a^{x}$ back into the equation:$\frac{dy}{dx} = a^{x} \log a$Alternatively,using the chain rule:$\frac{d}{dx}(a^{x}) = \frac{d}{dx}(e^{x \log a}) = e^{x \log a} \cdot \frac{d}{dx}(x \log a) = a^{x} \cdot \log a$.

Differentiate $a^{x}$ with respect to $x$,where $a$ is a positive constant.

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