Find the Tangent Line at the Point x^3+y^3-6xy=0 , (4/3,8/3)

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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.
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 chain rule, which states that is where and .
To apply the Chain Rule, set as .
Differentiate using the Power Rule which states that is where .
Replace all occurrences of with .
Rewrite as .
Evaluate .
Since is constant with respect to , the derivative of with respect to is .
Differentiate using the Product Rule which states that is where and .
Rewrite as .
Differentiate using the Power Rule which states that is where .
Multiply by .
Simplify.
Apply the distributive property.
Remove unnecessary parentheses.
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 .
Move all terms not containing to the right side of the equation.
Subtract from both sides of the equation.
Add to 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 .
Simplify .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify .
Simplify each term.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Cancel the common factor.
Rewrite the expression.
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.
Apply the product rule to .
Raise to the power of .
Raise to the power of .
Multiply .
Combine and .
Multiply by .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Move the negative in front of the fraction.
Simplify the denominator.
Apply the product rule to .
Raise to the power of .
Raise to the power of .
Multiply .
Combine and .
Multiply by .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Move the leading negative in into the numerator.
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Move the negative in front of the fraction.
Multiply .
Multiply by .
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 .
Apply the distributive property.
Combine and .
Multiply .
Multiply and .
Multiply by .
Multiply by .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Add and .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite in slope-intercept form.
Find the Tangent Line at the Point x^3+y^3-6xy=0 , (4/3,8/3)

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