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هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (نوفمبر 2014)

مشتقات الدوال الاعتيادية :

مجال الدالة ${\displaystyle D_{f}\,\!}$	الدالة ${\displaystyle f(x)\,\!}$	مجال المشتقة ${\displaystyle D_{f'}\,\!}$	المشتقة ${\displaystyle f'(x)\,\!}$	تعليق
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle k\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle 0\,\!}$	${\displaystyle k\in \mathbb {R} }$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle x\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle 1\,\!}$	حال ${\displaystyle x^{n}}$ عند ${\displaystyle n=1}$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle x^{2}\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle 2x\,\!}$	حالة ${\displaystyle n=2}$ عند ${\displaystyle x^{n}}$
${\displaystyle \mathbb {R} _{+}\,\!}$	${\displaystyle {\sqrt {x}}\,\!}$	${\displaystyle \mathbb {R} _{+}^{*}\,\!}$	${\displaystyle {\frac {1}{2{\sqrt {x}}}}\,\!}$	حالة ${\displaystyle x^{\alpha }}$ عند ${\displaystyle \alpha =1/2}$
${\displaystyle \mathbb {R} ^{*}\,\!}$	${\displaystyle {\frac {1}{x}}\,\!}$	${\displaystyle \mathbb {R} ^{*}\,\!}$	${\displaystyle -{\frac {1}{x^{2}}}\,\!}$	حالة ${\displaystyle 1/x^{n}}$ عند ${\displaystyle n=1}$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle x^{n}\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle nx^{n-1}\,\!}$	${\displaystyle n\in \mathbb {N} \,\!}$
${\displaystyle \mathbb {R} ^{*}\,\!}$	${\displaystyle {\frac {1}{x^{n}}}\,\!}$	${\displaystyle \mathbb {R} ^{*}\,\!}$	${\displaystyle -{\frac {n}{x^{n+1}}}\,\!}$	${\displaystyle n\in \mathbb {N} \,\!}$
${\displaystyle \mathbb {R} _{+}\,\!}$	${\displaystyle {\sqrt[{n}]{x}}\,\!}$	${\displaystyle \mathbb {R} _{+}^{*}\,\!}$	${\displaystyle {\frac {1}{n{\sqrt[{n}]{x^{n-1}}}}}\,\!}$	${\displaystyle n\in \mathbb {N} ~}$، حالة ${\displaystyle x^{\alpha }}$ عند ${\displaystyle \alpha =1/n}$
${\displaystyle \mathbb {R} _{+}\,\!}$	${\displaystyle x^{\alpha }\,\!}$	${\displaystyle \mathbb {R} _{+}\,\!}$	${\displaystyle \alpha x^{\alpha -1}\,\!}$	${\displaystyle \alpha \geq 1\,\!}$
${\displaystyle \mathbb {R} _{+}\,\!}$	${\displaystyle x^{\alpha }\,\!}$	${\displaystyle \mathbb {R} _{+}^{*}\,\!}$	${\displaystyle \alpha x^{\alpha -1}\,\!}$	${\displaystyle 0<\alpha <1\,\!}$
${\displaystyle \mathbb {R} _{+}^{*}\,\!}$	${\displaystyle x^{\alpha }\,\!}$	${\displaystyle \mathbb {R} _{+}^{*}\,\!}$	${\displaystyle \alpha x^{\alpha -1}\,\!}$	${\displaystyle \alpha <0\,\!}$
${\displaystyle \mathbb {R} ^{*}\,\!}$	${\displaystyle \ln |x|\,\!}$	${\displaystyle \mathbb {R} ^{*}\,\!}$	${\displaystyle {\frac {1}{x}}\,\!}$	حالة ${\displaystyle \log _{a}x}$ عتد a=e
${\displaystyle \mathbb {R} ^{*}\,\!}$	${\displaystyle \log _{a}|x|\,\!}$	${\displaystyle \mathbb {R} ^{*}\,\!}$	${\displaystyle {\frac {1}{x\ln a}}\,\!}$	${\displaystyle a>0\,\!}$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle e^{x}\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle e^{x}\,\!}$	حالة ${\displaystyle a^{x}}$ عند a=e
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle a^{x}\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle a^{x}\ln a\,\!}$	${\displaystyle a>0\,\!}$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle \sin x\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle \cos x\,\!}$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle \cos x\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle -\sin x\,\!}$
${\displaystyle \mathbb {R} \backslash \left({\frac {\pi }{2}}+\pi \mathbb {Z} \right)\,\!}$	${\displaystyle \tan x\,\!}$	${\displaystyle \mathbb {R} \backslash \left({\frac {\pi }{2}}+\pi \mathbb {Z} \right)\,\!}$	${\displaystyle {\frac {1}{\cos ^{2}x}}=1+\tan ^{2}x\,\!}$
${\displaystyle \mathbb {R} \backslash \left(\pi \mathbb {Z} \right)\,\!}$	${\displaystyle \cot x\,\!}$	${\displaystyle \mathbb {R} \backslash \left(\pi \mathbb {Z} \right)\,\!}$	${\displaystyle -{\frac {1}{\sin ^{2}x}}=-1-\cot ^{2}x\,\!}$
${\displaystyle [-1,1]\,\!}$	${\displaystyle \arcsin x\,\!}$	${\displaystyle ]-1,1[\,\!}$	${\displaystyle {\frac {1}{\sqrt {1-x^{2}}}}\,\!}$
${\displaystyle [-1,1]\,\!}$	${\displaystyle \arccos x\,\!}$	${\displaystyle ]-1,1[\,\!}$	${\displaystyle -{\frac {1}{\sqrt {1-x^{2}}}}\,\!}$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle \arctan x\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle {\frac {1}{1+x^{2}}}\,\!}$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle \operatorname {sh} x\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle \operatorname {ch} x\,\!}$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle \operatorname {ch} x\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle \operatorname {sh} x\,\!}$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle \operatorname {th} x\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle {\frac {1}{\operatorname {ch} ^{2}x}}\,\!}$
${\displaystyle \mathbb {R} \,\!}$	${\displaystyle \ \operatorname {argsh} \,x\,\!}$	${\displaystyle \mathbb {R} \,\!}$	${\displaystyle {\frac {1}{\sqrt {1+x^{2}}}}\,\!}$
${\displaystyle [1,+\infty [\,\!}$	${\displaystyle \ \operatorname {argch} \,x\,\!}$	${\displaystyle ]1,+\infty [\,\!}$	${\displaystyle {\frac {1}{\sqrt {x^{2}-1}}}\,\!}$
${\displaystyle ]-1,1[\,\!}$	${\displaystyle \ \operatorname {argth} \,x\,\!}$	${\displaystyle ]-1,1[\,\!}$	${\displaystyle {\frac {1}{1-x^{2}}}\,\!}$

إذا كانت ${\displaystyle g}$ إحدى تلك الدوال، فمشتقة الدالة المركبة ${\displaystyle x\mapsto g(cx)}$ (علما أن ${\displaystyle c}$ عدد حقيقي ثابت) هي ${\displaystyle x\mapsto cg'(cx)}$.

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هذه بذرة مقالة عن التحليل الرياضي بحاجة للتوسيع. فضلًا شارك في تحريرها.