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How do you find the derivative of Inverse trig function #y = arc csc (x/2)#?

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1 Answer

Aug 16, 2015

#2/ (x^2 sin x)#

Explanation:

#y=arc csc (x/2)#
#csc y = x/2#
#1/(cos y) = x/2#
#cos y = 2/x#

Diff wrt #x# on both sides:
#-sin y dy/dx = -2/x^2#
#dy/dx = 2/ (x^2 sin y)#
#d/dx arc csc (x/2) = 2/ (x^2 sin y)#

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