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AP Exams AP Calculus Derivatives Easy Practice Question

Learn + Solve: Shortcut, Trap & Fast Route Click to view shortcut, steps, and common mistake

Shortcut used: Identify the required derivative rule, differentiate symbolically, and verify signs and evaluation points.

Solve in 3 steps:

Mark the given values and the exact target.
Apply the relevant formula, rule, or concept.
Check the final value against the options.

Common mistake: Do not choose an option before confirming the exact demand of the question.

Question 3 Multiple Choice Question

Question

If f(x)=(x+1)/(x-1), what is f'(x)?

Explanation

Correct Answer: C

ANSWER

Correct Answer: C

Method / Topic: Derivatives

The quotient rule gives [(x-1)-(x+1)]/(x-1)^2=-2/(x-1)^2.

Why this answer is correct

The correct option matches the required rule and the given information.

Short Explanation

The quotient rule gives [(x-1)-(x+1)]/(x-1)^2=-2/(x-1)^2.

Detailed Explanation

Question

If f(x)=(x+1)/(x-1), what is f'(x)?

ANSWER

Correct Answer: C

Method / Topic: Derivatives

The quotient rule gives [(x-1)-(x+1)]/(x-1)^2=-2/(x-1)^2.

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Question 3

Easy Marks: 1.0 Practice Question

Learn + Solve: Shortcut, Trap & Fast Route Click to view shortcut, steps, and common mistake

Shortcut used: Identify the required derivative rule, differentiate symbolically, and verify signs and evaluation points.

Solve in 3 steps:

Mark the given values and the exact target.
Apply the relevant formula, rule, or concept.
Check the final value against the options.

Common mistake: Do not choose an option before confirming the exact demand of the question.

Question

If f(x)=(x+1)/(x-1), what is f'(x)?

Explanation

Correct Answer: C

ANSWER

Correct Answer: C

Method / Topic: Derivatives

The quotient rule gives [(x-1)-(x+1)]/(x-1)^2=-2/(x-1)^2.

Why this answer is correct

The correct option matches the required rule and the given information.

Short Explanation

The quotient rule gives [(x-1)-(x+1)]/(x-1)^2=-2/(x-1)^2.

Detailed Explanation

Question

If f(x)=(x+1)/(x-1), what is f'(x)?

ANSWER

Correct Answer: C

Method / Topic: Derivatives

The quotient rule gives [(x-1)-(x+1)]/(x-1)^2=-2/(x-1)^2.

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Identify the required derivative rule differentiate symbolically and verify signs and evaluation points.

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