Given equation: sin(xy) = cos(xy)

To find: dy/dx

Explanation:
To find dy/dx, we need to differentiate both sides of the equation with respect to x.

Differentiating sin(xy) with respect to x using the chain rule:

d(sin(xy))/dx = (d(sin(xy))/d(xy)) * (d(xy))/dx

Differentiating cos(xy) with respect to x using the chain rule:

d(cos(xy))/dx = (d(cos(xy))/d(xy)) * (d(xy))/dx

Since sin(xy) = cos(xy), the derivatives of sin(xy) and cos(xy) with respect to xy are equal. Therefore,

d(sin(xy))/d(xy) = d(cos(xy))/d(xy)

d(xy)/dx is the derivative of xy with respect to x, which can be found using the product rule:

d(xy)/dx = x * (d(y)/dx) + y * (d(x)/dx)

Key Points:
- Differentiate both sides of the equation with respect to x
- Apply the chain rule to differentiate sin(xy) and cos(xy) with respect to xy
- Set the derivatives of sin(xy) and cos(xy) equal to each other
- Use the product rule to differentiate xy with respect to x

Solving for dy/dx:
By substituting the derivatives into the differentiated equation, we have:

(d(sin(xy))/d(xy)) * (d(xy))/dx = (d(cos(xy))/d(xy)) * (d(xy))/dx

Since (d(xy))/dx is common on both sides, we can cancel it:

d(sin(xy))/d(xy) = d(cos(xy))/d(xy)

Now, we can cancel the common derivative with respect to xy:

d(sin(xy))/d(xy) = d(cos(xy))/d(xy) = k (where k is a constant)

This means that the derivative of sin(xy) with respect to xy is a constant, which implies that sin(xy) and cos(xy) differ by a constant factor.

Hence, the value of dy/dx is c (2).