Find dy/dx y^2+x^2=16

Problem

y2+x2=16

Solution

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

d(y2)/d(x)+d(x2)/d(x)=d(16)/d(x)

2. Apply the power rule and the chain rule to obtain the derivatives of each term.

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

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

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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