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If f(x) = e^(2x), what is f'(x)?

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Question: If f(x) = e^(2x), what is f\'(x)?

Options:

  1. 2e^(2x)
  2. e^(2x)
  3. 2x*e^(2x)
  4. e^(x)

Correct Answer: 2e^(2x)

Solution: 

Using the chain rule, f\'(x) = 2e^(2x).

If f(x) = e^(2x), what is f'(x)?

Practice Questions

Q1
If f(x) = e^(2x), what is f'(x)?
  1. 2e^(2x)
  2. e^(2x)
  3. 2x*e^(2x)
  4. e^(x)

Questions & Step-by-Step Solutions

If f(x) = e^(2x), what is f'(x)?
Correct Answer: 2e^(2x)
  • Step 1: Identify the function f(x) = e^(2x).
  • Step 2: Recognize that this is an exponential function where the exponent is a function of x (specifically, 2x).
  • Step 3: Recall the chain rule for differentiation, which states that if you have a function g(h(x)), the derivative is g'(h(x)) * h'(x).
  • Step 4: In our case, g(u) = e^u where u = 2x. The derivative of g(u) = e^u is g'(u) = e^u.
  • Step 5: Now find h'(x) where h(x) = 2x. The derivative h'(x) = 2.
  • Step 6: Apply the chain rule: f'(x) = g'(h(x)) * h'(x) = e^(2x) * 2.
  • Step 7: Simplify the expression: f'(x) = 2e^(2x).
  • Differentiation of Exponential Functions – Understanding how to differentiate functions of the form f(x) = e^(kx) using the chain rule.
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