أوراق غشّ لـ مشتقّات
حكم القوة
ddx (xa)=a·xa−1
مشتق ثابت
ddx (a)=0
قاعدة مجموع الفرق
(f±g)′=f′±g′
خروج ثابت
(a·f)′=a·f′
سيادة المنتج
(f·g)′=f′·g+f·g′
قاعدة الحاصل
(fg )′=f′·g−g′·fg2
حكم السلسلة
df(u)dx =dfdu ·dudx
ddx (ln(x))=1x
ddx (ln(|x|))=1x
ddx (ex)=ex
ddx (log(x))=1xln(10)
ddx (loga(x))=1xln(a)
ddx (sin(x))=cos(x)
ddx (cos(x))=−sin(x)
ddx (tan(x))=sec2(x)
ddx (sec(x))=tan(x)cos(x)
ddx (csc(x))=−cot(x)sin(x)
ddx (cot(x))=−1sin2(x)
ddx (arcsin(x))=1√1−x2
ddx (arccos(x))=−1√1−x2
ddx (arctan(x))=1x2+1
ddx (arcsec(x))=1√x2√x2−1
ddx (arccsc(x))=−1√x2√x2−1
ddx (arccot(x))=−1x2+1
ddx (sinh(x))=cosh(x)
ddx (cosh(x))=sinh(x)
ddx (tanh(x))=sech2(x)
ddx (sech(x))=tanh(x)(−sech(x))
ddx (csch(x))=−coth(x)csch(x)
ddx (coth(x))=−csch2(x)
ddx (arcsinh(x))=1√x2+1
ddx (arccosh(x))=1√x−1√x+1
ddx (arctanh(x))=11−x2
ddx (arcsech(x))=√2x+1 −1(x−1)x
ddx (arccsch(x))=−1√1x2 +1x2
ddx (arccoth(x))=11−x2
الجبر
مشتقّات
