What is the derivative of f(x) = arctan(e^(2x)) with respect to x?
Answer and explanation
Correct answer: A. 2 * e^(2x) / (1 + e^(4x))
- Step 1: By chain rule: d/dx [arctan(u)] = (1 / (1 + u^2)) (du/dx). Step 2. Here u = e^(2x), so du/dx = 2 e^(2x) and u^2 = (e^(2x))^2 = e^(4x). Step 3. Result = 2 e^(2x) / (1 + e^(4x)). Answer: 2 e^(2x) / (1 + e^(4x)). Why not the others:** Forgetting the factor of 2 gives e^(2x)/(1+e^(4x)).
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