\(\frac{dx}{dy} =−\frac{x}{y}\)

Since y is not on it's own side, we will have to differentiate implicitly. We will have to take the derivative with respect to x, since the question is asking for dydx dx/dy . After taking the derivative we get: \(2x+2y(dydx)=02x+2y\frac{dx}{dy}=0\)

Since we want to solve for dy/dx we must isolate it. First, we will subtract 2x from both sides to get: \(2y(dydx)=−2x2y\frac{dx}{dy}=−2x\)

Then we will divide both sides by 2y to get: \(dy/dx=−\frac{x}{y}\)

\(\frac{dx}{dy} =−\frac{x}{y}\)

Since y is not on it's own side, we will have to differentiate implicitly. We will have to take the derivative with respect to x, since the question is asking for dydx dx/dy . After taking the derivative we get: \(2x+2y(dydx)=02x+2y\frac{dx}{dy}=0\)

Since we want to solve for dy/dx we must isolate it. First, we will subtract 2x from both sides to get: \(2y(dydx)=−2x2y\frac{dx}{dy}=−2x\)

Then we will divide both sides by 2y to get: \(dy/dx=−\frac{x}{y}\)

\(\frac{dx}{dy} =−\frac{x}{y}\)