谁的导数是sinx分之一

回答
爱扬教育

2022-06-21

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y‘=1/sint
∫ydt=∫dt/sint
y=∫sindt/sin^2t=-∫dcost/(1-cos^2t)
=-(1/2)[∫dcost/(1-cost)+∫dcost/(1+cost)]
=-(1/2)ln[(1+cost)/(1-cost)]+c.

扩展资料

  基本初等函数的导数:

  1.y=c y'=0

  2.y=α^μ y'=μα^(μ-1)

  3.y=a^x y'=a^x lna

  y=e^x y'=e^x

  4.y=loga,x y'=loga,e/x

  y=lnx y'=1/x

  5.y=sinx y'=cosx

  6.y=cosx y'=-sinx

  7.y=tanx y'=(secx)^2=1/(cosx)^2

  8.y=cotx y'=-(cscx)^2=-1/(sinx)^2

  9.y=arc sinx y'=1/√(1-x^2)

  10.y=arc cosx y'=-1/√(1-x^2)

  11.y=arc tanx y'=1/(1+x^2)

  12.y=arc cotx y'=-1/(1+x^2)

  13.y=sh x y'=ch x

  14.y=ch x y'=sh x

  15.y=thx y'=1/(chx)^2

  16.y=ar shx y'=1/√(1+x^2)

  17.y=ar chx y'=1/√(x^2-1)

  18.y=ar th y'=1/(1-x^2)