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What is Derivatives of #y=sec(x)# ?

Question

What is Derivatives of #y=sec(x)# ?
What is Derivatives of #y=sec(x)# ?

Answers

#d/dx sec(x)=sec(x)tan(x)#

You could memorize this, but you can work it out too by knowing some trig properties.

The trig properties we will use are:
#sec (x)= 1/cos(x)#
and #sin x/cos x=tan x#

Deriving:
#d/dx sec (x) = d/dx 1/cos(x) = (cos (x)(0) - 1 (-sin (x)))/( cos (x)cos (x))# (using the quotient rule)
#= sin (x)/ (cos (x) cos (x)) = sin(x)/cos(x) *(1/cos( x)) = tan (x) sec( x)=sec (x) tan (x)#


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