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

Differentiate both sides of the equation.
Differentiate the left side of the equation.
Differentiate using the Product Rule which states that is where and .
The derivative of with respect to is .
Rewrite as .
Differentiate the right side of the equation.
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.
Solve for .
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)