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AP Calculus BC 3.4 Differentiating Inverse Trigonometric Functions Questions

Differentiate inverse trigonometric functions and use reciprocal derivative relationships to evaluate inverse-function slopes.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • identify the governing calculus relationship in the problem
  • justify the result with symbolic, graphical or contextual evidence

Covered syllabus points

FUN-3.E—Calculate derivatives of inverse and inverse trigonometric functions—Topic 3.4

Question 1

[Maximum number: 1]

If f(x)=sin⁡x+2x+1f(x)=\sin x+2 x+1 and g is the inverse function of f, what is the value of g′(1)g^{\prime}(1) ?

A

13\frac{1}{3}

B

1

C

3

D

12+cos⁡1\frac{1}{2+\cos 1}

E

2+cos⁡12+\cos 1

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