Find dy/dx x^3+y^3-6xy=0

Problem

x3+y3−6*x*y=0

Solution

1. Differentiate both sides of the equation with respect to x treating y as a function of x and applying the chain rule to the y3 term.

d(x3)/d(x)+d(y3)/d(x)−(d(6)*x*y)/d(x)=d(0)/d(x)

2. Apply the power rule and the product rule to the terms.

3*x2+3*y2d(y)/d(x)−(6*y+6*xd(y)/d(x))=0

3. Distribute the negative sign and group all terms containing d(y)/d(x) on one side of the equation.

3*x2+3*y2d(y)/d(x)−6*y−6*xd(y)/d(x)=0

3*y2d(y)/d(x)−6*xd(y)/d(x)=6*y−3*x2

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

d(y)/d(x)*(3*y2−6*x)=6*y−3*x2

5. Solve for d(y)/d(x) by dividing both sides by (3*y2−6*x)

d(y)/d(x)=(6*y−3*x2)/(3*y2−6*x)

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

d(y)/d(x)=(2*y−x2)/(y2−2*x)

Final Answer

d(y)/d(x)=(2*y−x2)/(y2−2*x)

Want more problems? Check here!