C′=0, where C is a constant
(C⋅x)′=C, where C is a constant
(xn)′=n⋅xn−1, x∈R, n∈Z
(xa)′=a⋅xa−1, x∈R, x>0, a∈R
(sinx)′=cosx
(cosx)′=−sinx
(tanx)′=(tg x)′=1/cos2x
(cotx)′=(cotg x)′=−1/sin2x
(arcsinx)′=1/√1−x2
(arccosx)′=−1/√1−x2
(arctan x)′=(arctg x)′=1/(1+x2)
(arccot x)′=(arccotg x)′=−1/(1+x2)
(ex)′=ex
(ax)′=ax⋅lna (a>0 is a constant)
(lnx)′=1/x
(logax)′=1/(x⋅lna) (a>0 is a constant)
(u+v)′=u′+v′
(u−v)′=u′−v′
(uv)′=u′⋅v+v′⋅u
(uv)′=u′v−v′uv2
(f(g(x)))′=f′(g(x))⋅g′(x)
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