Find dy/dx x^2+y^2=100

Problem

x2+y2=100

Solution

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

d(x2)/d(x)+d(y2)/d(x)=d(100)/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 the derivative 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 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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