Derivative of an exponential
Guided practice — solve each problem, check, then generate a fresh one.
Formula to apply
f(x) = a·e^{kx} → f′(x) = a·k·e^{kx}
Problem
Find f′(1) for f(x) = 1·e^{2x}. Give your answer to 3 decimal places.
Working
- 1Chain rule: f′(x) = 1·2·e^{2x} = 2·e^{2x}.
- 2e^{2·(1)} = e^{2} = 7.3891.
- 3f′(1) = 2 · 7.3891 = 14.778.