Find `dy/dx if y=(pi)/2-sinx`

Answer

To find \(\frac{dy}{dx}\) for the function \(y = \frac{\pi}{2} - \sin x\), we will follow these steps:

### Step 1: Write down the function
We start with the given function:
\[ y = \frac{\pi}{2} - \sin x \]

### Step 2: Differentiate with respect to \(x\)
To find \(\frac{dy}{dx}\), we differentiate both sides of the equation with respect to \(x\):
\[ \frac{dy}{dx} = \frac{d}{dx}\left(\frac{\pi}{2} - \sin x\right) \]

### Step 3: Apply the differentiation rules
Using the rules of differentiation:
- The derivative of a constant (like \(\frac{\pi}{2}\)) is \(0\).
- The derivative of \(-\sin x\) is \(-\cos x\).

Thus, we have:
\[ \frac{dy}{dx} = 0 - \cos x \]

### Step 4: Simplify the expression
This simplifies to:
\[ \frac{dy}{dx} = -\cos x \]

### Final Answer
Therefore, the derivative \(\frac{dy}{dx}\) is:
\[ \frac{dy}{dx} = -\cos x \]

---