$\frac{d}{dx}(x^2 e^x \sin x) = $

For some constants $a$ and $b$,find the derivative of $\frac{x-a}{x-b}$.

If $y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^{2} \alpha}\right)+\frac{1}{\sin ^{2} \alpha}}$ for $\alpha \in\left(\frac{3 \pi}{4}, \pi\right)$,then find $\frac{d y}{d \alpha}$ at $\alpha=\frac{5 \pi}{6}$.

$\frac{d}{dx} \log_{\sqrt{x}} \left(\frac{1}{x}\right)$ is equal to

If $y = \log(\sec(\tan^{-1} x))$ for $x > 0$,then the value of $\frac{dy}{dx}$ at $x = 1$ is:

If $y = \frac{\sin^{-1} x}{\sqrt{1 - x^2}}$,then $(1 - x^2)\frac{dy}{dx}$ is equal to