Mathematics - Differentiation Question with Solution | TestHub

$\frac{d}{dx}\left({\tan }^{-1}(\cos \sqrt{x})+{\sec }^{-1}\left({\mathrm{e}}^x\right)\right)$ $=\frac{(-\sin \sqrt{x})}{1+{\cos }^2\sqrt{x}}\cdot \left(\frac{1}{2\sqrt{x}}\right)+\frac{1}{e^x\sqrt{e^{2x}-1}}\cdot e^x$ but when $x=\frac{{\pi }^2}{4}$ $=-\frac{-\sin \frac{\pi }{2}}{1+{\cos }^2\frac{\pi }{2}}\left(\frac{1}{2}\right)\left(\frac{2}{\pi }\right)+\frac{1}{\sqrt{e^{{\pi }^2/2}-1}}$ $=-\frac{1}{\pi }+\frac{1}{\sqrt{e^{{\pi }^2/2}-1}}$