Summary table of derivatives
This page is a draft and is under active development.
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This page is a draft and is under active development.
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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) |
ddxxn=nxn−1 |
ddxex=ex |
ddxbx=bxln(b), where b>0 |
ddxln(|x|)=1x,x≠0 |
ddxlogb(|x|)=1xln(b), x≠0 |
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) |
ddxsin−1(x)=1√1−x2 |
ddxtan−1(x)=11+x2 |
ddxsec−1(x)=1|x|√x2−1 |
ddxcos−1(x)=−1√1−x2 |
ddxcot−1(x)=−11+x2 |
ddxcsc−1(x)=−1|x|√x2−1 |
ddx|x|=sgn(x)=x|x|,x≠0 |