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Differentiation Rules Integration Rulesddxxn=nxn-1 (power rule) xndx=xn+1n+1+Cddxun=nun-1u' cfxdx=cfxdxddxc=0 fx+g(x)dx=fxdx+gxdxddxcu=cu' Trigonometric Functions:ddxu±v=u'±v' sin xdx=-cos x+Cddxuv=uv'+vu' (product rule) cos xdx=sin x+Cddxuv=vu'-uv'v2 (quotient rule) tanx dx =-lncosx+Cg'x=1f'gx where g(x) is the inverse of f(x) cotx dx =lnsinx+CTrigonometric Functions: sec x dx=ln sec x+tan x+Cddxsin u=cosuu' ddxcos u=-sinuu' csc x dx=-ln csc x+cot u+Cddxtan u=sec2uu' ddxcot u=-csc2uu' sec2 xdx=tan x+Cddxsec u=sec u tan uu' ddxcsc u=-csc u cot uu' csc2 xdx=-cot x+CInverse Trigonometric Functions: sec x tan xdx=sec x+Cddxsin-1 u=u'1-u2 ddxcsc-1 u=-u'uu2-1 csc x cot xdx=-csc x+Cddxcos-1 u=-u'1-u2 ddxsec-1 u=u'uu2-1 Inverse Trigonometric Functions:ddxtan-1 u=u'1+u2 ddxcot-1 u=-u'1+u2 dua2-u2=sin-1ua+CExponential & Logarithmic Functions: dua2+u2=1atan-1ua+Cddxeu=euu' ddxau=ln aauu' duuu2-a2=1asec-1ua+Cddxu=uuu',u≠0 ddxlogau=u'ln au Exponential & Logarithmic Functions:Properties of Definite Integrals:exdx=ex+Caafxdx=0abfx=acfxdx+cbfxdx axdx=1ln aax+Cbafx=-abfxdx 1xdx=lnx+Cb1FORMULAS FROM GEOMETRYhθabcTriangleh=asinθA=12bhLaw of Cosinesc2=a2+b2-2abcosθhb2b1Trapezoid b2b1hA=h2b1+b2sEquilateral Trianglesh=s32sA=s234186880566675Area of a Sector A= θr22s=rθ(θ in radians)rCircular RingA=πR2-r2226314017145ConeV=13πr2hL.A.=πrlS.A.=πrl+πr21922145-2540SphereV=43πr3S.A.=4πr222059906985CylinderV=πr2hL.A.=2πrhS.A.=2πrh+2πr2Conic SectionsCirclerx-h2+y-k2=r2A=πr2C=2πrbaEllipse(x-h)2a2+(y-k)2b2=1A=πabC=2πa2+b22Parabola171451210310Hyperbola ................
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