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What is the derivative of f(x) = e^(2x)?
What is the derivative of f(x) = e^(2x)?
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Practice Questions
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Q1
What is the derivative of f(x) = e^(2x)?
2e^(2x)
e^(2x)
e^(x)
2x*e^(2x)
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Using the chain rule, f'(x) = d/dx(e^(2x)) = 2e^(2x).
Questions & Step-by-step Solutions
1 item
Q
Q: What is the derivative of f(x) = e^(2x)?
Solution:
Using the chain rule, f'(x) = d/dx(e^(2x)) = 2e^(2x).
Steps: 7
Show Steps
Step 1: Identify the function you want to differentiate, which is f(x) = e^(2x).
Step 2: Recognize that this function is an exponential function where the exponent is 2x.
Step 3: Recall the chain rule, 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, we need to find the derivative of g(x).
Step 5: Differentiate g(x) = 2x. The derivative g'(x) = 2.
Step 6: Now apply the chain rule: f'(x) = e^(g(x)) * g'(x) = e^(2x) * 2.
Step 7: Simplify the expression: f'(x) = 2e^(2x).
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