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Real Analysis - Basic Differentiation Rules

C=0, where C is a constant

(Cx)=C, where C is a constant

(xn)=nxn1, xR, nZ

(xa)=axa1, xR, x>0, aR

(sinx)=cosx

(cosx)=sinx

(tanx)=(tg x)=1/cos2x

(cotx)=(cotg x)=1/sin2x

(arcsinx)=1/1x2

(arccosx)=1/1x2

(arctan x)=(arctg x)=1/(1+x2)

(arccot x)=(arccotg x)=1/(1+x2)

(ex)=ex

(ax)=axlna    (a>0 is a constant)

(lnx)=1/x

(logax)=1/(xlna)    (a>0 is a constant)


(u+v)=u+v

(uv)=uv

(uv)=uv+vu

(uv)=uvvuv2

(f(g(x)))=f(g(x))g(x)


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