How do you find the derivative of #y=csc^-1 (x/2)#?

Question

2324 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-03T09:30:36

#(dy)/(dx)=-2/(xsqrt(x^2-4))#

As #y=csc^(-1)(x/2)#

#x/2=cscy#

taking derivative on both sides

#1/2=-cotycscy*(dy)/(dx)#

or #(dy)/(dx)=-1/2*1/coty*1/cscy#

= #-1/2*1/sqrt(csc^2y-1)*1/cscy#

= #-1/2*1/sqrt(x^2/4-1)*2/x#

= #-2/(xsqrt(x^2-4))#