导数相关知识总结

2021-05-06 本文已影响0人 Super小牛

基本初等函数的导数

${(C)}'=0$
${(x^{n})}'=nx^{n-1}$
${(a^{x})}'=a^{x}\ln(a)$
${(e^{x})}'=e^{x}$
${(\log(a^{x}))}'=\frac{1}{x\ln(a)}$
${(\ln(x))}'=\frac{1}{x}$
${(\sin(x))}'=\cos(x)$
${(\cos(x))}'=-\sin(x)$
${(\tan(x))}'=\sec^{2}(x)$
${(\cot(x))}'=-\csc^{2}(x)$
${(\sec(x))}'=\sec(x)\tan(x)$
${(\csc(x))}'=-\csc(x)\cot(x)$
${(\arcsin(x))}'=\frac{1}{ \sqrt{1-x^{2}}}$
${(\arccos(x))}'=-\frac{1}{ \sqrt{1-x^{2}}}$
${(\arctan(x))}'=\frac{1}{1+x^{2}}$
${(\arccot(x))}'=- \frac{1}{1+x^{2}}$