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

Find dy/dx e^ysin(x)=x+xy
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 .
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 the right side of the equation.
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.
Solve for .
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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