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How do you differentiate # (sec(πx))/(tan(πx))#?

1 Answer

Aug 28, 2016

#= -pi csc pi x cot pi x#

Explanation:

#d/dx (sec(πx))/(tan(πx))#

#=d/dx (cos pi x)/(cos pi x sin pi x)#

#=d/dx ( sin pi x)^(-1) [= d/dx csc pi x]#

by power and chain rules
#= -( sin pi x)^(-2) * cos pi x * pi#

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

#= -pi csc pi x cot pi x#

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