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Mathematics LibreTexts

Summary table of derivatives

This page is a draft and is under active development. 

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Differentiation Rules

Sum Rule

ddx(f(x)+g(x))=(f(x)+g(x))=f(x)+g(x)

Constant Multiple Rule ddx(cf(x))=(cf(x))=cf(x)
Product Rule ddx(f(x)g(x))=(f(x)g(x))=f(x)g(x)+f(x)g(x)
ddx(1f(x))=f(x)(f(x))2
Quotient Rule ddx(f(x)g(x))=(f(x)g(x))=g(x)f(x)f(x)g(x)(g(x))2
Chain Rule ddxf(g(x))=(f(g(x)))=f(g(x))g(x)

Derivatives for Elementary Trancendental Functions

ddxxn=nxn1
ddxex=ex
ddxbx=bxln(b), where b>0
ddxln(|x|)=1x,x0
ddxlogb(|x|)=1xln(b), x0
ddxsin(x)=cos(x)
ddxcos(x)=sin(x)
ddxtan(x)=sec2(x)
ddxsec(x)=sec(x)tan(x)
ddxcsc(x)=csc(x)cot(x)
ddxcot(x)=csc2(x)
ddxsin1(x)=11x2
ddxtan1(x)=11+x2
ddxsec1(x)=1|x|x21
ddxcos1(x)=11x2
ddxcot1(x)=11+x2
ddxcsc1(x)=1|x|x21
ddx|x|=sgn(x)=x|x|,x0

 


This page titled Summary table of derivatives is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Pamini Thangarajah.

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