Find dy/dx 3x^2-2y^2=5

Problem

3*x2−2*y2=5

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(3)*x2)/d(x)−(d(2)*y2)/d(x)=d(5)/d(x)

2. Apply the power rule to 3*x2 and the chain rule to 2*y2

6*x−4*yd(y)/d(x)=0

3. Isolate the term containing d(y)/d(x) by subtracting 6*x from both sides.

−4*yd(y)/d(x)=−6*x

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

d(y)/d(x)=(−6*x)/(−4*y)

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

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

Final Answer

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

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