Let $x y = 4$ and $\frac{d y}{d t} = 3$ Find $\frac{d x}{d t}$ when $x = 4$

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Final Answer: The rate of change of $x$ with respect to $t$ when $x = 4$ is $- 12$ .

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Step 1 ：Given the equation $x y = 4$ , we can differentiate both sides with respect to $t$ to get $x \frac{d y}{d t} + y \frac{d x}{d t} = 0$ .

Step 2 ：We are given that $\frac{d y}{d t} = 3$ and we need to find $\frac{d x}{d t}$ when $x = 4$ .

Step 3 ：We can substitute $x = 4$ into the original equation to find the corresponding value of $y$ . So, $y = \frac{4}{x} = 1$ .

Step 4 ：Then we can substitute these values into the differentiated equation to solve for $\frac{d x}{d t}$ . So, $4 * 3 + 1 * \frac{d x}{d t} = 0$ . Solving this equation gives $\frac{d x}{d t} = - 12$ .

Step 5 ：Final Answer: The rate of change of $x$ with respect to $t$ when $x = 4$ is $- 12$ .

Let xy=4 and dydt=3 Find dxdt when x=4

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Let $x y = 4$ and $\frac{d y}{d t} = 3$ Find $\frac{d x}{d t}$ when $x = 4$