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A derivative is simply a rate of change. Whether you're modeling the movement of a particle or a supply/demand model, this is a key instrument of Calculus.

If \(\displaystyle f(x)=\frac{1}{x},\) what is \(f'(x)\)?

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If \(\displaystyle f(x)=\frac{1}{x^3},\) what is \(f'(x)\)?

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If \(\displaystyle f(x)=\frac{-7x}{x^2+7},\) what is the value of \( f'(3)?\)

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If \(\displaystyle f(x)=\frac{x-22}{x^2+1},\) what is the value of \(f'(-1)?\)

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If \(\displaystyle f(x)=\frac{4}{x^2},\) what is \(f'(x)\)?

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