# Find the Tangent Line at the Point xe^y+ye^x=1 , (0,1)

,
Find and evaluate at and to find the slope of the tangent line at and .
Differentiate both sides of the equation.
Differentiate the left side of the equation.
By the Sum Rule, the derivative of with respect to is .
Evaluate .
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 .
Differentiate using the Exponential Rule which states that is where =.
Replace all occurrences of with .
Rewrite as .
Differentiate using the Power Rule which states that is where .
Multiply by .
Evaluate .
Differentiate using the Product Rule which states that is where and .
Differentiate using the Exponential Rule which states that is where =.
Rewrite as .
Reorder terms.
Since is constant with respect to , the derivative of with respect to is .
Reform the equation by setting the left side equal to the right side.
Solve for .
Reorder factors in .
Move all terms not containing to the right side of the equation.
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 .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Simplify each term.
Move the negative in front of the fraction.
Move the negative in front of the fraction.
Simplify terms.
Combine the numerators over the common denominator.
Factor out of .
Factor out of .
Factor out of .
Simplify the expression.
Rewrite as .
Move the negative in front of the fraction.
Replace with .
Evaluate at and .
Replace the variable with in the expression.
Replace the variable with in the expression.
Simplify the numerator.
Multiply by .
Anything raised to is .
Simplify.
Simplify the denominator.
Simplify.
Multiply by .
Anything raised to is .
Simplify by multiplying through.
Divide by .
Apply the distributive property.
Multiply by .
Plug in the slope of the tangent line and the and values of the point into the pointslope formula .
Simplify.
The slope-intercept form is , where is the slope and is the y-intercept.
Rewrite in slope-intercept form.
Multiply by .
Simplify .
Subtract from .
Apply the distributive property.
Rewrite as .
Move .
Rewrite as .
Add to both sides of the equation.
Find the Tangent Line at the Point xe^y+ye^x=1 , (0,1)