Find dy/dx x^2+4y^2=36

Problem

x2+4*y2=36

Solution

1. Differentiate both sides 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(36)/d(x)

2. Apply the power rule to x2 and the chain rule to 4*y2

2*x+8*yd(y)/d(x)=0

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

8*yd(y)/d(x)=−2*x

4. Solve for dy/dx by dividing both sides by 8*y

d(y)/d(x)=(−2*x)/(8*y)

5. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 2

d(y)/d(x)=−x/(4*y)

Final Answer

d(y)/d(x)=−x/(4*y)

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