CUET Preparation Today
Differentiate the function $\cos^{-1}(e^x)$ with respect to $x$. |
$\frac{e^x}{\sqrt{1-e^{2x}}}$ $\frac{-e^x}{\sqrt{1-e^x}}$ $\frac{-e^x}{\sqrt{1-e^{2x}}}$ $\frac{-1}{\sqrt{1-e^{2x}}}$ |
$\frac{-e^x}{\sqrt{1-e^{2x}}}$ |
The correct answer is Option (3) → $\frac{-e^x}{\sqrt{1-e^{2x}}}$ ## Let $y = \cos^{-1}(e^x)$. Using chain rule, we have $\frac{dy}{dx} = \frac{-1}{\sqrt{1-(e^x)^2}} \cdot \frac{d}{dx}(e^x) = \frac{-e^x}{\sqrt{1-e^{2x}}}$ |
