-
-| $f(x)$ | $f^\prime(x)$ |
-| ------ | ------------- |
-| $x^n$ | $nx^{n-1}$ |
-| $kx^n$ | $knx^{n-1}$ |
-| $g(x) + h(x)$ | $g^\prime (x) + h^\prime (x)$ |
-| $c$ | $0$ |
-| ${u \over v}$ | ${{v{du \over dx} - u{dv \over dx}} \over v^2}$ |
-| $uv$ | $u{dv \over dx} + v{du \over dx}$ |
-| $f \circ g$ | ${dy \over du} \cdot {du \over dx}$ |
-
+\begin{tabularx}{\columnwidth}{rl}
+
+ \hline \(f(x)\) & \(f^\prime(x)\) \\ \hline
+
+ \(kx^n\) & \(knx^{n-1}\)\tabularnewline
+ \(g(x) \pm h(x)\) & \(g^\prime (x) \pm h^\prime (x)\)\tabularnewline
+ \(c\) & \(0\)\tabularnewline
+ \({u \over v}\) &
+ \({{(v{du \over dx} - u{dv \over dx}}) \div v^2}\)\tabularnewline
+ \(uv\) & \(u{dv \over dx} + v{du \over dx}\)\tabularnewline
+ \(f \circ g\) & \({dy \over du} \cdot {du \over dx}\)\tabularnewline
+ \(\sin ax\) & \(a\cos ax\)\tabularnewline
+ \(\sin(f(x))\) & \(f^\prime(x) \cdot \cos(f(x))\)\tabularnewline
+ \(\cos ax\) & \(-a \sin ax\)\tabularnewline
+ \(\cos(f(x))\) & \(f^\prime(x)(-\sin(f(x)))\) \\
+ \(e^{ax}\) & \(ae^{ax}\)\tabularnewline
+ \(\log_e {ax}\) & \(1 \over x\)\tabularnewline
+ \(\log_e f(x)\) & \(f^\prime (x) \over f(x)\)\tabularnewline
+
+ \hline
+
+\end{tabularx}