Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers) :
`sin(x+a)`

Answer

To find the derivative of the function \( y = \sin(x + a) \), we will follow the steps of differentiation using the chain rule.

### Step-by-Step Solution:

1. **Identify the function**: We have the function \( y = \sin(x + a) \). Here, \( x + a \) is the argument of the sine function.

2. **Apply the chain rule**: The chain rule states that if you have a composite function \( y = \sin(u) \) where \( u = x + a \), the derivative \( \frac{dy}{dx} \) can be found using:
\[ \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} \]

3. **Differentiate the outer function**: The derivative of \( \sin(u) \) with respect to \( u \) is:
\[ \frac{dy}{du} = \cos(u) \]

4. **Differentiate the inner function**: The derivative of \( u = x + a \) with respect to \( x \) is:
\[ \frac{du}{dx} = 1 \]

5. **Combine the derivatives**: Now, substituting back into the chain rule:
\[ \frac{dy}{dx} = \cos(x + a) \cdot 1 = \cos(x + a) \]

6. **Final answer**: Therefore, the derivative of the function \( y = \sin(x + a) \) is:
\[ \frac{dy}{dx} = \cos(x + a) \]