## Final Answer

## Step-by-step Solution

Problem to solve:

Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

Learn how to solve implicit differentiation problems step by step online.

$\frac{d}{dx}\left(x\right)=\frac{d}{dx}\left(\sin\left(y\right)+1\right)$

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative (d/dx)(x=sin(y)+1). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (1) is equal to zero.