Evaluate differentiation of y with respect to x :
`y=sinxcosx`

Explanation

To evaluate the differentiation of \( y \) with respect to \( x \) for the function \( y = \sin x \cos x \), we will use the product rule of differentiation. The product rule states that if you have two functions multiplied together, say \( u \) and \( v \), then the derivative of their product is given by:

\[ \frac{d}{dx}(uv) = u \frac{dv}{dx} + v \frac{du}{dx} \]

In our case, we can identify:
- \( u = \sin x \)
- \( v = \cos x \)

Now, we will differentiate \( y \) step by step.

### Step 1: Differentiate \( u \) and \( v \)
First, we find the derivatives of \( u \) and \( v \):
- The derivative of \( u = \sin x \) is:
\[ \frac{du}{dx} = \cos x \]
- The derivative of \( v = \cos x \) is:
\[ \frac{dv}{dx} = -\sin x \]

### Step 2: Apply the Product Rule
Now we apply the product rule:
\[ \frac{dy}{dx} = u \frac{dv}{dx} + v \frac{du}{dx} \]
Substituting \( u \), \( v \), \( \frac{du}{dx} \), and \( \frac{dv}{dx} \):
\[ \frac{dy}{dx} = \sin x (-\sin x) + \cos x (\cos x) \]

### Step 3: Simplify the Expression
Now we simplify the expression:
\[ \frac{dy}{dx} = -\sin^2 x + \cos^2 x \]

### Step 4: Final Result
Thus, the differentiation of \( y \) with respect to \( x \) is:
\[ \frac{dy}{dx} = \cos^2 x - \sin^2 x \]