How do you differentiate #y=csc^-1(3x)#?

1 Answer
mason m
Nov 25, 2016

Rewrite since #csc^-1# is an inverse function.

#csc(y)=3x#

Differentiate both sides. On the left-hand side, don't forget that the chain rule will apply.

#-csc(y)cot(y)dy/dx=3#

Note that on the left-hand side, #csc(y)=3x#. Also note that #cot(y)=sqrt(csc^2(y)-1)=sqrt(9x^2-1)#.

#-3xsqrt(9x^2-1)dy/dx=3#

#dy/dx=-1/(xsqrt(9x^2-1))#

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