find the derivative of the function y=csc^-1(sec x)

Answer 1

First you need to know the derivative of inverse cosecant. From there, it is a chain rule problem.

So, d/dx of arccsc(f(x)) = -1/[ | f(x) | *sqrt((f(x))²-1)] * f'(x)

So, in our case, f(x) = sec(x)

We get -1/[ | sec(x) | * sqrt(sec²(x) -1)] * sec(x)*tan*(x)