Derivatives of Exponential Functions
Explore and practice finding derivatives of exponential functions, including those with base e and other bases, and applications in calculus.
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Derivatives of Exponential Functions
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Read each question carefully and show all your work. Simplify your answers where possible.
1. Find the derivative of the function f(x) = 3e^x.
2. Differentiate y = 5^(2x).
3. Which of the following is the derivative of f(x) = e^(4x)?
e^(4x)
4e^(4x)
(1/4)e^(4x)
4xe^(4x)
4. The derivative of a^u with respect to x is .
5. The population of a bacterial colony is given by P(t) = 1000e^(0.05t), where t is the time in hours. Find the rate of change of the population at t = 10 hours.
6. The derivative of e^x is xe^(x-1).
True
False
7. Find dy/dx if y = x^2 * e^x.
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