x^{2} +y^{2} =25 What is dydx dx/dy?

x^{2} +y^{2} =25 What is dydx dx/dy?

Question
Differential equations
asked 2021-02-09
\(x^{2} +y^{2} =25\)
What is dydx dx/dy?

Answers (1)

2021-02-10
\(\frac{dx}{dy} =−\frac{x}{y}\)
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: \(dy/dx=−\frac{x}{y}\)
\(\frac{dx}{dy} =−\frac{x}{y}\)
0

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