三角関数の微分公式と問題例 | 高校数学の美しい物語

(sin⁡x)′=cos⁡x(cos⁡x)′=−sin⁡x(tan⁡x)′=1cos⁡2x(Arcsin x)′=11−x2(Arccos x)′=−11−x2(Arctan x)′=11+x2 \begin{aligned} (\sin x)' &= \cos x\\ (\cos x)' &= -\sin x\\ (\tan x)' &= \dfrac{1}{\cos^2 x}\\ (\mathrm{Arcsin}~ x)' &= \dfrac{1}{\sqrt{1-x^2}}\\ (\mathrm{Arccos}~ x)' &= -\dfrac{1}{\sqrt{1-x^2}}\\ (\mathrm{Arctan}~ x)' &= \dfrac{1}{1+x^2}\\ \end{aligned} (sinx)′(cosx)′(tanx)′(Arcsin x)′(Arccos x)′(A