AP Calculus AB · Unit 2: Differentiation: Definition and Fundamental Properties
2.7 Derivatives of cos x, sin x, e^x, and ln x
In short
You are expected to know and apply the specific derivative rules for sine, cosine, exponential (e^x), and natural logarithmic (ln x) functions. Beyond straightforward calculation, the course requires you to recognize when a given limit expression represents the formal definition of a derivative for one of these familiar functions.
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What else do you need to know about Derivatives of cos x, sin x, e^x, and ln x?
By identifying the underlying function and the point at which the derivative is being evaluated, you can determine the limit's value using derivative rules rather than algebraic limit evaluation techniques.
Can you do these?
- I can calculate the derivatives of sine, cosine, exponential, and logarithmic functions.
How is Derivatives of cos x, sin x, e^x, and ln x tested on the exam?
On the AP Exam, you will be assessed on your ability to calculate derivatives of these familiar functions both in isolation and as foundational steps within more complex problems (e.g., applying product, quotient, or chain rules). A common conceptual question style involves presenting a limit that matches the difference quotient definition of a derivative for sine, cosine, e^x, or ln x. You must recognize this structure and evaluate the limit by taking the derivative of the known function, rather than attempting to evaluate the limit directly. Precision with notation and avoiding arithmetic errors when applying these rules is critical.
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Derivatives of cos x, sin x, e^x, and ln x: common questions
What do you need to know about Derivatives of cos x, sin x, e^x, and ln x for AP Calculus AB?
You are expected to know and apply the specific derivative rules for sine, cosine, exponential (e^x), and natural logarithmic (ln x) functions. Beyond straightforward calculation, the course requires you to recognize when a given limit expression represents the formal definition of a derivative for one of these familiar functions.
How is Derivatives of cos x, sin x, e^x, and ln x tested on the AP Calculus AB exam?
On the AP Exam, you will be assessed on your ability to calculate derivatives of these familiar functions both in isolation and as foundational steps within more complex problems (e.g., applying product, quotient, or chain rules).
How do I know I have mastered Derivatives of cos x, sin x, e^x, and ln x?
Check you can do each of these: calculate the derivatives of sine, cosine, exponential, and logarithmic functions.
Where does Derivatives of cos x, sin x, e^x, and ln x fit in AP Calculus AB?
Derivatives of cos x, sin x, e^x, and ln x is topic 2.7 in Unit 2: Differentiation: Definition and Fundamental Properties of AP Calculus AB.
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