Find dy/dx x^2-y^3=0

Problem

d()/d(x)*(x2−y3=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 y term.

d(x2)/d(x)−d(y3)/d(x)=d(0)/d(x)

2. Apply the power rule to the x term and the chain rule to the y term.

2*x−3*y2d(y)/d(x)=0

3. Isolate the term containing d(y)/d(x) by subtracting 2*x from both sides.

−3*y2d(y)/d(x)=−2*x

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

d(y)/d(x)=(−2*x)/(−3*y2)

5. Simplify the signs in the resulting fraction.

d(y)/d(x)=(2*x)/(3*y2)

Final Answer

d(y)/d(x)=(2*x)/(3*y2)

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