Chapter 2 - Differentiation - 2.5 Exercises - Page 145: 14

$\dfrac{dy}{dx}=\dfrac{1}{1-\csc^2{y}}.$

$\dfrac{d}{dx}(\cot{y})=\dfrac{d}{dx}(x)-\dfrac{d}{dx}(y)\rightarrow$ $\dfrac{dy}{dx}(-\csc^2{y})=1-\dfrac{dy}{dx}\rightarrow$ $1=\dfrac{dy}{dx}(1-\csc^2{y})\rightarrow$ $\dfrac{dy}{dx}=\dfrac{1}{1-\csc^2{y}}.$