Evaluate differentiation of y with respect to x.
`((2)/(sinx))`

Explanation

To evaluate the differentiation of \( y \) with respect to \( x \) for the function \( y = \frac{2}{\sin x} \), we will follow these steps:

### Step 1: Rewrite the function
We start with the function:
\[ y = \frac{2}{\sin x} \]
This can be rewritten using the reciprocal function:
\[ y = 2 \cdot \csc x \]

### Step 2: Differentiate using the product rule
To differentiate \( y \) with respect to \( x \), we will use the chain rule and the fact that the derivative of \( \csc x \) is \( -\csc x \cot x \):
\[ \frac{dy}{dx} = 2 \cdot \frac{d}{dx}(\csc x) \]

### Step 3: Apply the derivative of \( \csc x \)
Now we apply the derivative:
\[ \frac{dy}{dx} = 2 \cdot (-\csc x \cot x) \]

### Step 4: Simplify the expression
Thus, we simplify the expression:
\[ \frac{dy}{dx} = -2 \csc x \cot x \]

### Final Answer
The differentiation of \( y \) with respect to \( x \) is:
\[ \frac{dy}{dx} = -2 \csc x \cot x \]

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