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) = 2·e^{2x}. Give your answer to 3 decimal places.
Working
- 1Chain rule: f′(x) = 2·2·e^{2x} = 4·e^{2x}.
- 2e^{2·(-1)} = e^{-2} = 0.13534.
- 3f′(-1) = 4 · 0.13534 = 0.54134.