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′(-2) for f(x) = 3·e^{3x}. Give your answer to 3 decimal places.
Working
- 1Chain rule: f′(x) = 3·3·e^{3x} = 9·e^{3x}.
- 2e^{3·(-2)} = e^{-6} = 0.0024788.
- 3f′(-2) = 9 · 0.0024788 = 0.022309.