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

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

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

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

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

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