Derivative of sin(c+1)-y-1,5

1. Differentiate $\left(- y + \sin{\left(c + 1 \right)}\right) - \frac{3}{2}$ term by term:

   1. Differentiate $- y + \sin{\left(c + 1 \right)}$ term by term:

      1. Let $u = c + 1$.

      2. The derivative of sine is cosine:

         $$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$$

      3. Then, apply the chain rule. Multiply by $\frac{d}{d y} \left(c + 1\right)$:

         1. The derivative of the constant $c + 1$ is zero.

         The result of the chain rule is:

         $$0$$

      4. The derivative of a constant times a function is the constant times the derivative of the function.

         1. Apply the power rule: $y$ goes to $1$

         So, the result is: $-1$

      The result is: $-1$

   2. The derivative of the constant $- \frac{3}{2}$ is zero.

   The result is: $-1$

The answer is:

$$-1$$