Find dy/dx 2x^2-3y^2=4

Problem

2*x2−3*y2=4

Solution

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

(d(2)*x2)/d(x)−(d(3)*y2)/d(x)=d(4)/d(x)

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

4*x−6*yd(y)/d(x)=0

3. Isolate the term containing d(y)/d(x) by subtracting 4*x from both sides.

−6*yd(y)/d(x)=−4*x

4. Solve for the derivative by dividing both sides by −6*y

d(y)/d(x)=(−4*x)/(−6*y)

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

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

Final Answer

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

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