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.)

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Answer

Final Answer: $11.7$

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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: $11.7$

Given y=x. Find dxdt when y=3 and dydt=1.95dxdt=(Simplify your answer.)

Answer

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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.)