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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.

If \(f(x)=2x+5,\) what is the value of \(f'(3)?\)

If \[f(x)=x^2+7x,\] what is the value of \(f'(6)?\)

Find the derivative of \(f(x)=13x^3\) using the definition of derivative

\[ f'(x) = \lim_{h \rightarrow 0 } \frac{ f( x + h) - f(x) } { h }. \]

Find the derivative of \(f(x)=-2x^2+3x+26\) from the definition

\[ f'(x) = \lim_{h \rightarrow 0 } \frac{ f( x + h) - f(x) } { h } .\]

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