工程表格/导数性质

	导数	条件
1	${\frac {d}{dx}}c=0$
2	${\frac {d}{dx}}(cx)=c$
3 基本幂法则	${\frac {d}{dx}}(x^{n})=nx^{n-1}$
4 求和法则	${\frac {d}{dx}}\left(f\pm g\pm h\pm \cdots \right)={\frac {df}{dx}}\pm {\frac {dg}{dx}}\pm {\frac {dh}{dx}}\pm \cdots$
5 常数倍乘法则	${\frac {d}{dx}}(cf)=c{\frac {df}{dx}}$
6 乘积法则	${\frac {d}{dx}}(fg)=f{\frac {dg}{dx}}+g{\frac {df}{dx}}$
6 乘积法则（扩展）	${\frac {d}{dx}}(fgh)=fg{\frac {dh}{dx}}+fh{\frac {dg}{dx}}+gh{\frac {df}{dx}}$
7 商法则	${\frac {d}{dx}}\left({\frac {f}{g}}\right)={\frac {g{\frac {df}{dx}}-f{\frac {dg}{dx}}}{g^{2}}}$	$g\neq 0\,$
8 链式法则	${\frac {df}{dx}}={\frac {df}{dg}}\cdot {\frac {dg}{dx}}$
9	${\frac {d}{dx}}\left(f^{n}\right)=nf^{n-1}{\frac {df}{dx}}$
10 倒数法则	${\frac {d}{dx}}\left({\frac {1}{f}}\right)=-{\frac {1}{f^{2}}}{\frac {df}{dx}}$	$f\neq 0\,$
11 函数幂法则	${\frac {d}{dx}}\left(f^{g}\right)={\frac {d}{dx}}\left(e^{g\ln f}\right)=f^{g}\left({\frac {g}{f}}\cdot {\frac {df}{dx}}+{\frac {dg}{dx}}\ln f\right)$	$f>0\,$
12 对数法则	${\frac {df}{dx}}=f{\frac {d}{dx}}\left(\ln f\right)$	$f>0\,$
13 反函数法则	${\frac {df}{dx}}={\frac {1}{\frac {dx}{df}}}$	${\frac {dx}{df}}\neq 0\,$
备注	f, g, h 是 x 的函数 c, n 是常数。