# Derivative of Implicit Multivariable Function – Calculating first and second order derivatives to a one-variable function – Exercise 3104

Exercise

The equation

$$y-2\sin y=x$$

Defines the implicit function

$$y(x)$$

Find its first and second order derivatives y'(x), y”(x).

$$y'(x)=\frac{1}{1-2\cos y}$$
$$y''(x)=\frac{-2\sin y}{{(1-2\cos y)}^3}$$