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

Math
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Find and evaluate at and to find the slope of the tangent line at and .
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Differentiate both sides of the equation.
Differentiate the left side of the equation.
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By the Sum Rule, the derivative of with respect to is .
Evaluate .
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Differentiate using the Product Rule which states that is where and .
Differentiate using the chain rule, which states that is where and .
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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 .
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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 .
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Reorder factors in .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from both sides of the equation.
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify .
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Simplify each term.
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Move the negative in front of the fraction.
Move the negative in front of the fraction.
Simplify terms.
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Combine the numerators over the common denominator.
Factor out of .
Factor out of .
Factor out of .
Simplify the expression.
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Rewrite as .
Move the negative in front of the fraction.
Replace with .
Evaluate at and .
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Replace the variable with in the expression.
Replace the variable with in the expression.
Simplify the numerator.
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Multiply by .
Anything raised to is .
Simplify.
Simplify the denominator.
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Simplify.
Multiply by .
Anything raised to is .
Add and .
Simplify by multiplying through.
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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.
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The slope-intercept form is , where is the slope and is the y-intercept.
Rewrite in slope-intercept form.
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Multiply by .
Simplify .
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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)

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