Find dy/dx x^3+y^3=6xy

Problem

x^3+y^3=6*x*y

Solution

1. Differentiate both sides with respect to x treating y as a function of x and applying the chain rule to the y^3 term.

d(x^3)/d(x)+d(y^3)/d(x)=(d(6)*x*y)/d(x)

2. Apply the power rule to the left side and the product rule to the right side.

3*x^2+3*y^2d(y)/d(x)=6*y+6*xd(y)/d(x)

3. Group the terms containing d(y)/d(x) on one side of the equation and the remaining terms on the other side.

3*y^2d(y)/d(x)−6*xd(y)/d(x)=6*y−3*x^2

4. Factor out the common d(y)/d(x) term.

d(y)/d(x)*(3*y^2−6*x)=6*y−3*x^2

5. Solve for the derivative by dividing both sides by the expression in parentheses.

d(y)/d(x)=(6*y−3*x^2)/(3*y^2−6*x)

6. Simplify the fraction by dividing the numerator and the denominator by 3

d(y)/d(x)=(2*y−x^2)/(y^2−2*x)

Final Answer

d(y)/d(x)=(2*y−x^2)/(y^2−2*x)

Want more problems? Check here!