A. \(2 x+10\) B. \(-x / 1\) C. \(y^{2} / \sqrt{ }\) D. \(10-x^{2}\)
Correct Answer: B
Explanation
Given: \(x^{2}+y^{2}=10\) Solution method - 1: We solve for \(y\) to get the function in the form that we are used to dealing with and then differentiate. i.e. \(x^{2}+y^{2}=10\) \begin{array}{l} y^{2}=10-x^{2} \\ y=\sqrt{10-x^{2}} \\ y=\left(10-x^{2}\right)^{1 / 2} \end{array}ifferentiating this, we obtain \begin{aligned} \frac{d y}{d x} &=\frac{1}{2}(-2 x)\left(10-x^{2}\right)^{-1 / 2} \\ \frac{d y}{d x} &=\frac{-x}{\sqrt{10-x^{2}}} \\ \text { but } y &=\sqrt{10-x^{2}} \\ & \therefore \frac{d y}{d x}=\frac{-x}{y} \end{aligned}