The derivative of

$$ y=(1-x)(2-x) \ldots \ldots \ldots \ldots \ldots \ldots(\mathrm{n}-x) $$

at $x=1$ is

If $X \sim B(n, p)$ then $\frac{P(X=k)}{P(X=k-1)}=$

The differential equation of all straight lines passing through the point $(1,-1)$ is

The first derivative of the function $\left(\cos ^{-1}\left(\sin \sqrt{\frac{1+x}{2}}\right)+x^x\right)$ with respect to $x$ at $x=1$ is