Differentiate the following with respect to $x$: $e^{-x}$

If $y=\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\log \sqrt{1-x^2}$,then $\frac{d y}{d x}=$

Let $m$ and $n$ be odd integers such that $0 < m < n$. If $f(x) = x^{\frac{m}{n}}$ for $x \in \mathbb{R}$,then:

People living on Mars,instead of the usual definition of derivative $D f(x)$,define a new kind of derivative,$D^*f(x)$ by the formula $D^*f(x) = \lim_{h \to 0} \frac{f^2(x + h) - f^2(x)}{h}$ where $f^2(x)$ means $[f(x)]^2$. If $f(x) = x \ln x$,then the value of $\left. D^*f(x) \right|_{x = e}$ is:

$f(x)$ is differentiable on $\mathbb{R}$ and $f^{\prime}(m) \neq 0, \,m \in \mathbb{R}$. If $\lim _{x \rightarrow m} \frac{x f(m)-m f(x)}{x-m}+f^{\prime}(m)=f(m)$,then $m=$

Find the derivative of the following function: $\frac{\cos x}{1+\sin x}$