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d dx k= 0 (1) ddx [f(x)±g(x)] =f?(x)±g?(x) (2) ddx [k·f(x)] =k·f?(x) (3) ddx [f(x)g(x)] =f(x)g?(x) +g(x)f?(x) (4) ddx f(x)g(x)? =g(x)f?(x)-f(x)g?(x)[g(x)]2(5) ddx f(g(x)) =f?(g(x))·g?(x) (6) ddx xn=nxn-1(7) ddx sinx= cosx(8) ddx cosx=-sinx(9) ddx tanx= sec2x(10) ddx cotx=-csc2x(11) ddx secx= secxtanx(12) ddx cscx=-cscxcotx(13) ddx ex=ex(14) ddx ax=axlna(15) ddx ln|x|=1x (16) ddx sin-1x=1⎷1-x2(17) ddx cos-1x=-1⎷1-x2(18) ddx tan-1x=1x

2+ 1(19)

ddx cot-1x=-1x

2+ 1(20)

ddx sec-1x=1|x|⎷x

2-1(21)

ddx csc-1x=-1|x|⎷x

2-1(22)Integration Formulas

dx=x+C(1) x ndx=xn+1n+ 1+C(2) dxx = ln|x|+C(3) e xdx=ex+C(4) a xdx=1lnaax+C(5) lnxdx=xlnx-x+C(6) sinxdx=-cosx+C(7) cosxdx= sinx+C(8) tanxdx=-ln|cosx|+C(9) cotxdx= ln|sinx|+C(10) secxdx= ln|secx+ tanx|+C(11) cscxdx=-ln|cscx+ cotx|+C(12) sec

2xdx= tanx+C(13)

csc

2xdx=-cotx+C(14)

secxtanxdx= secx+C(15) cscxcotxdx=-cscx+C(16) dx⎷a

2-x2= sin-1xa

+C(17) dxa

2+x2=1a

tan-1xa +C(18) dxx ⎷x

2-a2=1a

sec-1|x|a +C(19)quotesdbs_dbs7.pdfusesText_13

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