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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.

Derivative by First Principle

         

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

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

\(f(x)\) is a function differentiable at \(x=1\) and \(f'(1)=\frac{1}{15}\). What is the value of \[\displaystyle \lim_{x \to 1} \frac{x^3-1}{f(x)-f(1)}?\]

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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