# Find dy First, divide dx e to the power of ysin(x) equals x plus xy

Differentiate both sides of the equation.

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

The derivative of with respect to is .

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

To apply the Chain Rule, set as .

Differentiate using the Exponential Rule which states that is where =.

Replace all occurrences of with .

Should be rewritten as .

Shift terms.

Differentiate.

By the Sum Rule, the derivative of with respect to is .

Differentiate using the Power Rule which states that is where .

Evaluate .

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

Rewrite as .

Differentiate using the Power Rule which states that is where .

First, multiply by .

Shift terms.

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

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 .

Factor out of .

Divide each term by and simplify.

Divide each term in by .

The common factor should be canceled of .

Cancel the common factor.

Divide by .

Replace with .

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