Differentiate

Question

Y = 1/SinX^2

Answer 1

the way you typed it, Wolfram read it as
http://www.wolframalpha.com/input/?i=+Y+%3D+1%2FSinX%5E2

and y = (sinx)^-2
dy/dx = -2(sinx)^-3 (cosx)
= -2cotx /sin^2 x
or
= -2cotx csc^2 x

if you meant:
y = 1/ sin(x^2)
then y = sin(x^2)^-1
dy/dx = -1sin(x^2)^-2 cos(x^2) (2x)
= -2x cot(x^2) csx(x^2)