今日の微分2020/9/231 min読了の目安(約200字)IDEAアイデア記事math#katex三角関数の微分 (sinxsinx+cosx)′=cosx(sinx+cosx)−sinx(cosx−sinx)(sinx+cosx)2=sinxcosx+cos2x−sinxcosx+sin2x(sinx+cosx)2=1(sinx+cosx)2\begin{aligned} \left(\frac{\sin x}{\sin x+\cos x}\right)'&=\frac{\cos x(\sin x+\cos x)-\sin x(\cos x-\sin x)}{(\sin x+\cos x)^2}\\ &=\frac{\sin x\cos x+\cos^2x-\sin x\cos x+\sin^2x}{(\sin x+\cos x)^2}\\ &=\bm{\frac{1}{(\sin x+\cos x)^2}} \end{aligned}(sinx+cosxsinx)′=(sinx+cosx)2cosx(sinx+cosx)−sinx(cosx−sinx)=(sinx+cosx)2sinxcosx+cos2x−sinxcosx+sin2x=(sinx+cosx)21 KaTeX\KaTeXKATEXで書けるんだ!