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y=sECx求导

解由 y=secx 得y'=(secx)'=(1/cosx)' =[1'cosx-1(cosx)']/cos^2x =sinx/cos^2x 则y''=[sinx/cos^2x]' =[(sinx)'cos^2x-sin(cos^2x)']/cos^4x =[cosxcos^2x-2sinxcosx(cosx)']/cos^4x =[cos^3x+2sin^2xcosx]/cos^4x =[cos^2x+2sin^2x]/cos^3x

y'=(secx)'tanx+secx(tanx)'=(secxtanx)tanx+secx(secx)^2=secx[(tanx)^2+(secx)^2]=2*(tanx)^3

y=(secx)^3 y'=3(secx)^2*(secx)' =3(secx)^2*secx*tanx =3tanx(secx)^3

sinx除以cos2x的平方

如图

y = sec² x y' = 2 sec x sec x tanx = 2 sec³ x sin x = 2 sinx / cos³ x...... 记住几个公式: sec x = 1/cos x (sec x)' = sec x tan x = sinx/cos²x

3sin  cosx

y=ln(secx+tanx) 那么求导得到 y'=1/(secx+tanx) *(secx+tanx)' =1/(secx+tanx) *[secx *tanx +(secx)^2)] =secx

y=cscxsecx=(1/sinx)(1/cosx)=2/(2sinxcosx)=2/sin2x=2(sin2x)^-1y'=2(-1)(sin2x)^-2 * 2 =-4/(sin2x)^2

y=(secx)^3 y'=3(secx)^2*(secx)' =3(secx)^2*secx*tanx =3tanx(secx)^3

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