Higher-order derivatives

Exercise

1.: Show that the following formula．
(a): $\displaystyle{(\sin{x})^{(n)} = \sin{(x + \frac{n \pi}{2})}}$
(b): $\displaystyle{(\cos{x})^{(n)} = \cos{(x + \frac{n \pi}{2})}}$
(c): $\displaystyle{\left[(1 + x)^{\alpha}\right]^{(n)} = \alpha(\alpha -1)\cdots(\alpha - n + 1)(1+x)^{\alpha - n}}$
2.: Find the th derivative of the following function．
(a): $\displaystyle{f(x) = \frac{x^{3}}{1 - x}}$
(b): $\displaystyle{f(x) = x^{2} \sin{x}}$
(c): $\displaystyle{f(x) = e^{x} \sin{x}}$