Differentiate both sides of the equation.

Differentiate using the Product Rule which states that is where and .

The derivative of with respect to is .

Rewrite as .

Differentiate using the Product Rule which states that is where and .

Differentiate using the chain rule, which states that is where and .

To apply the Chain Rule, set as .

The derivative of with respect to is .

Replace all occurrences of with .

Rewrite as .

Differentiate using the Power Rule which states that is where .

Multiply by .

Reform the equation by setting the left side equal to the right side.

Reorder factors in .

Reorder factors in .

Subtract from both sides of the equation.

Subtract from both sides of the equation.

Factor out of .

Factor out of .

Factor out of .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Replace with .

Find dy/dx ysin(x)=xsin(y)