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Section 12.2 Using Function Notation
If you have properly defined a function
\(f(x)\text{,}\) you may also make use of the familiar
\(f'(x)\) notation used in class.
\begin{equation*}
\displaystyle f\, := \,x\mapsto \sin \left( x \right) +{x}^{2}
\end{equation*}
\begin{equation*}
\displaystyle \cos \left( x \right) +2\,x
\end{equation*}
This notation is especially useful for evaluating the derivative at a value, without using the
subs() command separately.
Aside While using
\(m\) is a common choice for slope, it is a good idea to avoid overusing it in your Maple worksheet. You may wish to use
\(m1\text{,}\) \(m2\text{,}\) etc. when calculating the slopes of many tangent lines.
\begin{equation*}
\displaystyle slope\mathit{1}\, := \, 1
\end{equation*}
\begin{equation*}
\displaystyle slope\mathit{2}\, := \, -1 + 2\pi
\end{equation*}
Higher derivatives are also notated in much the same way as in class.
\begin{equation*}
\displaystyle -\sin \left( x \right) +2
\end{equation*}
Rather than using a string of tick marks, we use a raised exponent in parentheses to specify the
\(n\) th derivative. This notation can only be used in 2D Math mode.
\begin{equation*}
\displaystyle -\cos \left( x \right)
\end{equation*}
