The demand $x$ is the number of items that can be sold at a price of $p$. For $x = p^2 - 7p + 900$, find the rate of change of $p$ with respect to $x$ by differentiating implicitly. The rate of change of the price $p$ with respect to the demand $x$ is $\boxed{}$.
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We want to find $\frac{dp}{dx}$. We differentiate both sides of the equation with respect to $x$: $\frac{dx}{dx} = \frac{d}{dx}(p^2 - 7p + 900)$ $1 = 2p \frac{dp}{dx} - 7 \frac{dp}{dx} + 0$ $1 = (2p - 7) \frac{dp}{dx}$ $\frac{dp}{dx} = \frac{1}{2p - 7}$ Show more…
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Find the rate of change of $p$ with respect to $x$ by differentiating implicitly $(x$ is the number of items that can be sold at a price of $\$ p$ ). $$ x=p^{2}-2 p+1,000 $$
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