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If f(x) = e^(2x), what is f'(x)?
If f(x) = e^(2x), what is f'(x)?
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Practice Questions
1 question
Q1
If f(x) = e^(2x), what is f'(x)?
2e^(2x)
e^(2x)
2x*e^(2x)
e^(x)
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Using the chain rule, f'(x) = 2e^(2x).
Questions & Step-by-step Solutions
1 item
Q
Q: If f(x) = e^(2x), what is f'(x)?
Solution:
Using the chain rule, f'(x) = 2e^(2x).
Steps: 7
Show Steps
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).
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