Find dy/dx 3xy-x^2-4=0

Problem

3*x*y−x2−4=0

Solution

1. Differentiate both sides of the equation with respect to x treating y as a function of x

d()/d(x)*(3*x*y−x2−4)=d()/d(x)*0

2. Apply the product rule to the term 3*x*y where the derivative of x*y is xd(y)/d(x)+y(1)

3*(xd(y)/d(x)+y)−2*x−0=0

3. Distribute the constant through the parentheses.

3*xd(y)/d(x)+3*y−2*x=0

4. Isolate the term containing d(y)/d(x) by moving all other terms to the right side of the equation.

3*xd(y)/d(x)=2*x−3*y

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

d(y)/d(x)=(2*x−3*y)/(3*x)

Final Answer

d(y)/d(x)=(2*x−3*y)/(3*x)

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