Find dy/dx x^2-4y^2-9=0

Problem

x2−4*y2−9=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 term involving y

d(x2)/d(x)−(d(4)*y2)/d(x)−d(9)/d(x)=d(0)/d(x)

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

2*x−8*yd(y)/d(x)−0=0

3. Isolate the term containing d(y)/d(x) by moving 2*x to the right side of the equation.

−8*yd(y)/d(x)=−2*x

4. Solve for d(y)/d(x) by dividing both sides by −8*y

d(y)/d(x)=(−2*x)/(−8*y)

5. Simplify the resulting fraction by dividing the numerator and denominator by their greatest common factor, −2

d(y)/d(x)=x/(4*y)

Final Answer

d(y)/d(x)=x/(4*y)

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