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

Problem

x2−y2=5

Solution

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

d(x2)/d(x)−d(y2)/d(x)=d(5)/d(x)

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

2*x−2*yd(y)/d(x)=0

3. Isolate the term containing d(y)/d(x) by subtracting 2*x from both sides.

−2*yd(y)/d(x)=−2*x

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

d(y)/d(x)=(−2*x)/(−2*y)

5. Simplify the resulting fraction by canceling the common factor of −2

d(y)/d(x)=x/y

Final Answer

d(y)/d(x)=x/y

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