Given $y=\sqrt{x}$. Find $\frac{d x}{d t}$ when $y=3$ and $\frac{d y}{d t}=1.95$ $\frac{d x}{d t}=$ (Simplify your answer.)

Step 1 ：We are given the function \(y=\sqrt{x}\) and we are asked to find \(\frac{d x}{d t}\) when \(y=3\) and \(\frac{d y}{d t}=1.95\).

Step 2 ：We can rewrite \(y=\sqrt{x}\) as \(y=x^{1/2}\). The derivative of \(y\) with respect to \(x\) is \(\frac{1}{2}x^{-1/2}\).

Step 3 ：We are given that \(\frac{d y}{d t}=1.95\). We can use the chain rule to express this in terms of \(\frac{d x}{d t}\): \(\frac{d y}{d t} = \frac{d y}{d x} \cdot \frac{d x}{d t}\).

Step 4 ：We can solve this equation for \(\frac{d x}{d t}\): \(\frac{d x}{d t} = \frac{d y}{d t} / \frac{d y}{d x}\).

Step 5 ：We can substitute the given values and the derivative we found into this equation to find \(\frac{d x}{d t}\).

Step 6 ：Final Answer: \(\boxed{11.7}\)