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Derivatives Cheat Sheet

 

Derivatives Rules

Power Rule ddx (xa)=a·xa1
Derivative of a constant ddx (a)=0
Sum Difference Rule (f±g)=f±g
Constant Out (a·f)=a·f
Product Rule (f·g)=f·g+f·g
Quotient Rule (fg )=f·gg·fg2 
Chain rule df(u)dx =dfdu ·dudx 


Common Derivatives

ddx (ln(x))=1x  ddx (ln(|x|))=1x 
ddx (ex)=ex ddx (log(x))=1xln(10) 
ddx (loga(x))=1xln(a) 


Trigonometric Derivatives

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) 


Arc Trigonometric Derivatives

ddx (arcsin(x))=11x2  ddx (arccos(x))=11x2 
ddx (arctan(x))=1x2+1  ddx (arcsec(x))=1x2x21 
ddx (arccsc(x))=1x2x21  ddx (arccot(x))=1x2+1 


Hyperbolic Derivatives

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)


Arc Hyperbolic Derivatives

ddx (arcsinh(x))=1x2+1  ddx (arccosh(x))=1x1x+1 
ddx (arctanh(x))=11x2  ddx (arcsech(x))=2x+1 1(x1)x 
ddx (arccsch(x))=11x2 +1x2  ddx (arccoth(x))=11x2