導関数の計算(calculation of derivatives)

演習問題

1.: 次の関数の導関数を求めよう．
(a): $\displaystyle{y = \frac{3x-1}{x^{2} + 1}}$
(b): $\displaystyle{y = \sec{x}}$
(c): $\displaystyle{y = {\rm cosec}{x}}$
(d): $\displaystyle{y = \cot{x}}$
2.: 次の関数の導関数を求めよう．
(a): $\displaystyle{y = \sin{(x^{2} + 1)}}$
(b): $\displaystyle{y = \cos{(\sqrt{x + 1})}}$
(c): $\displaystyle{y = e^{\sin{x}}}$