Question #66881

1 Answer
sente
Oct 13, 2016

#d/dxtan(x) = sec^2(x)#

Explanation:

Using the quotient rule along with the derivatives for sine and cosine

  • #d/dx sin(x) = cos(x)#
  • #d/dx cos(x) = -sin(x)#

we have

#d/dxtan(x) = d/dxsin(x)/cos(x)#

#=(cos(x)(d/dxsin(x))-sin(x)(d/dxcos(x)))/cos^2(x)#

#=(cos(x)(cos(x))-sin(x)(-sin(x)))/cos^2(x)#

#=(cos^2(x)+sin^2(x))/cos^2(x)#

#=1/cos^2(x)#

#=(1/cos(x))^2#

#=sec^2(x)#

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