Find dy/dx y^2-x^3=22

Problem

y2−x3=22

Solution

1. Differentiate both sides with respect to x treating y as a function of x and applying the chain rule to the y2 term.

d(y2)/d(x)−d(x3)/d(x)=d(22)/d(x)

2. Apply the power rule and the chain rule to compute the derivatives.

2*yd(y)/d(x)−3*x2=0

3. Isolate the term containing d(y)/d(x) by adding 3*x2 to both sides of the equation.

2*yd(y)/d(x)=3*x2

4. Solve for dy/dx by dividing both sides by 2*y

d(y)/d(x)=(3*x2)/(2*y)

Final Answer

d(y)/d(x)=(3*x2)/(2*y)

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