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What is the first derivative of f(x) = e^(2x)?

Practice Questions

Q1
What is the first derivative of f(x) = e^(2x)?
  1. 2e^(2x)
  2. e^(2x)
  3. e^(x)
  4. 2x*e^(2x)

Questions & Step-by-Step Solutions

What is the first derivative of f(x) = e^(2x)?
  • Step 1: Identify the function f(x) = e^(2x).
  • Step 2: Recognize that this is an exponential function where the exponent is 2x.
  • Step 3: Recall the chain rule for differentiation, which states that if you have a function of the form e^(g(x)), the derivative is e^(g(x)) * g'(x).
  • Step 4: In our case, g(x) = 2x. Now, find the derivative of g(x).
  • Step 5: The derivative of g(x) = 2x is g'(x) = 2.
  • Step 6: Apply the chain rule: f'(x) = e^(2x) * g'(x) = e^(2x) * 2.
  • Step 7: Simplify the expression: f'(x) = 2e^(2x).
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