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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the derivative of f(x) = e^x?
💡 Hint: Refer to the specific property of e.
Question 2
Easy
Calculate the derivative of f(x) = 2^x.
💡 Hint: Remember to multiply by ln(base).
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the derivative of f(x) = e^x?
- e^x
- 2e^x
- 1
💡 Hint: Think about how e behaves under differentiation.
Question 2
For what base does f(x) = a^x have a derivative formula of f'(x) = a^x ln(a)?
- True
- False
💡 Hint: Recall the derivative formula for constants.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
If a turtle population grows exponentially, represented by P(t) = P0 e^(kt), where k is a constant. If at t = 0, P0 = 1000 and k = 0.03, find the population after 5 years.
💡 Hint: Remember the formula for population growth!
Question 2
Given the function f(x) = 3^x, find an x-value such that the slope of the tangent line at that point equals 20.
💡 Hint: You will have to use logarithms to isolate x.
Challenge and get performance evaluation