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Monday, February 11, 2013

 

Trig Function Derivatives

  ddxsin(x)=cos(x)ddxtan(x)=sec2(x)ddxsec(x)=sec(x)tan(x)   ddxcos(x)=sin(x)ddxcot(x)=csc2(x)ddxcsc(x)=csc(x)cot(x)

  ddxsin1(x)=11x2ddxtan1(x)=11+x2ddxsec1(x)=1xx21   ddxcos1(x)=11x2ddxcot1(x)=11+x2ddxcsc1(x)=1xx21

Take the last trig function as an example. Let f(x)=csc1(x),

  f(csc(x))=csc1(csc(x))=xf(csc(x))csc(x)=1f(csc(x))=1csc(x)=1csc(x)cot(x)
Since sin2(x)+cos2(x)=1, divide both sides by sin2(x):
  1+cot2(x)=csc2(x)cot(x)=csc2(x)1
From above,
  f(csc(x))=1csc(x)cot(x)f(csc(x))=1csc(x)csc2(x)1f(x)=1xx21

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