CUET Preparation Today
Differentiate $a^x$ w.r.t. $x$, where $a$ is a positive constant. |
$x a^{x-1}$ $\frac{a^x}{\ln a}$ $a^x \ln a$ $a^x$ |
$a^x \ln a$ |
The correct answer is Option (3) → $a^x \ln a$ ## Let $y = a^x$. Then $\log y = x \log a$ Differentiating both sides w.r.t. $x$, we have $\frac{1}{y} \frac{dy}{dx} = \log a$ or $\frac{dy}{dx} = y \log a$ Thus $\frac{d}{dx}(a^x) = a^x \log a$ |
