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Calculate the derivative of f(x) = e^(2x).
Calculate the derivative of f(x) = e^(2x).
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Practice Questions
1 question
Q1
Calculate the derivative of f(x) = e^(2x).
2e^(2x)
e^(2x)
2xe^(2x)
e^(x)
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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: Calculate 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 a composition of two functions: the outer function e^u (where u = 2x) and the inner function u = 2x.
Step 3: Apply the chain rule, which states that the derivative of e^u with respect to x is e^u times the derivative of u with respect to x.
Step 4: Differentiate the outer function e^u. The derivative of e^u is e^u itself.
Step 5: Differentiate the inner function u = 2x. The derivative of 2x is 2.
Step 6: Combine the results from the chain rule: f'(x) = e^(2x) * 2.
Step 7: Simplify the expression: f'(x) = 2e^(2x).
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