,

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 point–slope formula .

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)