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# Derivatives

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.

# Derivatives of Rational Function

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

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

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

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

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

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