Derivative rules from a table of values practice problems
Product, quotient and chain rules when you only know values of f, g and their derivatives. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Use the table to find \( \displaystyle h'(2) \) for \( \displaystyle h(x) = - 2 f(x) + 4 g(x) \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 2 & -2 & -4 & -1 & 3\end{array} \]
Use the table to find \( \displaystyle h'(0) \) for \( \displaystyle h(x) = \frac{f(x)}{g(x)} \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 0 & 3 & 4 & 4 & 2\end{array} \]
Use the table to find \( \displaystyle h'(2) \) for \( \displaystyle h(x) = 4 f(x) + 2 g(x) \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 2 & -2 & 1 & 3 & -4\end{array} \]
Use the table to find \( \displaystyle h'(2) \) for \( \displaystyle h(x) = - f(x) + 2 g(x) \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 2 & -3 & 2 & 5 & -1\end{array} \]
Use the table to find \( \displaystyle h'(2) \) for \( \displaystyle h(x) = \frac{f(x)}{g(x)} \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 2 & -4 & 1 & -3 & -2\end{array} \]
Use the table to find \( \displaystyle h'(3) \) for \( \displaystyle h(x) = f(x) g(x) \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 3 & 4 & -3 & 4 & -1\end{array} \]
Use the table to find \( \displaystyle h'(2) \) for \( \displaystyle h(x) = x f(x) + \left[g(x)\right]^{2} \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 2 & 4 & 1 & 1 & -2\end{array} \]
Use the table to find \( \displaystyle h'(2) \) for \( \displaystyle h(x) = \frac{f(x)}{g(x)} \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 2 & -4 & -3 & 4 & 3\end{array} \]
Use the table to find \( \displaystyle h'(0) \) for \( \displaystyle h(x) = f(x) g(x) \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 0 & 4 & 2 & 2 & -1\end{array} \]
Use the table to find \( \displaystyle h'(0) \) for \( \displaystyle h(x) = f(x) g(x) \). \[ \begin{array}{c|cccc} x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 0 & -5 & -2 & 3 & 3\end{array} \]