Differentiate the following functions w.r.t. x:
`sin x/(3)`

Answer

To differentiate the function \( y = \frac{\sin x}{3} \) with respect to \( x \), we can follow these steps:

### Step 1: Identify the function
Let \( y = \frac{\sin x}{3} \).

### Step 2: Factor out the constant
Since \( \frac{1}{3} \) is a constant, we can factor it out of the differentiation:
\[ y = \frac{1}{3} \sin x \]

### Step 3: Differentiate using the constant multiple rule
Now, we differentiate \( y \) with respect to \( x \):
\[ \frac{dy}{dx} = \frac{1}{3} \frac{d}{dx}(\sin x) \]

### Step 4: Apply the differentiation formula
We know that the derivative of \( \sin x \) is \( \cos x \):
\[ \frac{dy}{dx} = \frac{1}{3} \cos x \]

### Step 5: Write the final answer
Thus, the derivative of the function \( y = \frac{\sin x}{3} \) with respect to \( x \) is:
\[ \frac{dy}{dx} = \frac{1}{3} \cos x \]

### Summary
The final answer is:
\[ \frac{dy}{dx} = \frac{1}{3} \cos x \]

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