כלל השרשרת :
(f(g(x))′=f′(g(x))⋅g(x)′{\displaystyle (f(g(x))'=f'(g(x))\cdot g(x)'}
1x=x−1fn(x)=n⋅fn−1(x)⋅f′(x)cf(x)′=−c∗f′(x)f(x)2(f(x))′=f(x)′−12=−12f−12−1(x)⋅f′(x)=12f(x)⋅f′(x){\displaystyle {\begin{aligned}{\frac {1}{x}}&=x^{-1}\\f^{n}(x)&=n\cdot f^{n-1}(x)\cdot f'(x)\\{\frac {c}{f(x)}}'=-{\frac {c*f'(x)}{f(x)^{2}}}\\({\sqrt {f(x)}})'=f(x)'^{-{\frac {1}{2}}}&=-{\frac {1}{2}}f^{-{\frac {1}{2}}-1}(x)\cdot f'(x)={\frac {1}{2{\sqrt {f(x)}}}}\cdot f'(x)\end{aligned}}}
sin(f(x))′=cosf(x)⋅f′(x)cos(f(x))′=−sinf(x)⋅f′(x)tan(f(x))′=sin(f(x))cos(f(x))′=f′(x)cos2f(x){\displaystyle {\begin{aligned}\sin(f(x))'&=\cos f(x)\cdot f'(x)\\\cos(f(x))'&=-\sin f(x)\cdot f'(x)\\\tan(f(x))'&={\frac {\sin(f(x))}{\cos(f(x))}}'={\frac {f'(x)}{\cos ^{2}f(x)}}\end{aligned}}}
arcsinf(x)′=f(x)′1−f(x)2arccosf(x)′=−f(x)′)1−f(x)2arctanf(x)′=f′(x)1+f2(x){\displaystyle {\begin{aligned}\arcsin f(x)'&={\frac {f(x)'}{\sqrt {1-f(x)^{2}}}}\\\arccos f(x)'&=-{\frac {f(x)')}{\sqrt {1-f(x)^{2}}}}\\\arctan f(x)'&={\frac {f'(x)}{1+f^{2}(x)}}\end{aligned}}}
(ef(x))′=ef(x)⋅f′(x)(af(x))′=af(x)⋅lna⋅f′(x)ln(f(x))′=f′(x)f(x)logaf(x)′=f′(x)f(x)⋅lna{\displaystyle {\begin{aligned}(e^{f(x)})'&=e^{f(x)}\cdot f'(x)\\(a^{f(x)})'&=a^{f(x)}\cdot \ln a\cdot f'(x)\\\ln(f(x))'&={\frac {f'(x)}{f(x)}}\\\log _{a}f(x)'&={\frac {f'(x)}{f(x)\cdot \ln a}}\end{aligned}}}