Find dy/dx 4x^2-y^2=5

Problem

4*x2−y2=5

Solution

1. Differentiate both sides with respect to x using the chain rule for the term involving y

(d(4)*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.

8*x−2*yd(y)/d(x)=0

3. Isolate the term containing d(y)/d(x) by subtracting 8*x from both sides.

−2*yd(y)/d(x)=−8*x

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

d(y)/d(x)=(−8*x)/(−2*y)

5. Simplify the fraction by dividing the numerator and denominator by −2

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

Final Answer

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

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