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

Problem

x2+y2=36

Solution

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

d()/d(x)*(x2+y2)=d(36)/d(x)

2. Apply the sum rule and the power rule to the left side, using the chain rule for the term involving y

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 the derivative by dividing both sides by 2*y

d(y)/d(x)=(−2*x)/(2*y)

5. Simplify the 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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