Question

If y = sin^-1(e^x) + cos^-1(e^x), then $\frac{dy}{dx}$ = ____________________.

Answer 1

$y={\sin }^{-1}\left(e^x\right)+{\cos }^{-1}\left(e^x\right)$

$\Rightarrow y=\frac{\mathrm{\pi }}{2}$ $\left({\sin }^{-1}x+{\cos }^{-1}x=\frac{\mathrm{\pi }}{2}\right)$

Differentiating both sides with respect to x, we get

$\frac{dy}{dx}=\frac{d}{dx}\left(\frac{\mathrm{\pi }}{2}\right)$

$\Rightarrow \frac{dy}{dx}=0$


If y = sin⁻¹(e^x) + cos⁻¹(e^x), then $\frac{dy}{dx}$ = ____0____.