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AP Calculus AB 3.4 Differentiating Inverse Trigonometric Functions Questions

Review AP Calculus AB 3.4 by applying inverse-trigonometric derivative formulas, checking their domains, and simplifying values at specified inputs.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • apply derivative formulas for inverse trigonometric functions
  • evaluate inverse-trigonometric derivatives at specified points

Covered syllabus points

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

Question 1

[Maximum number: 1]

ddx(tan⁡−1x+2x)=\frac{d}{d x}\left(\tan ^{-1} x+2 \sqrt{x}\right)=

A

−1sin⁡2x+1x-\frac{1}{\sin ^{2} x}+\frac{1}{\sqrt{x}}

B

11−x2−4x3\frac{1}{\sqrt{1-x^{2}}}-4 \sqrt[3]{x}

C

11−x2+1x\frac{1}{\sqrt{1-x^{2}}}+\frac{1}{\sqrt{x}}

D

11+x2−4x3\frac{1}{1+x^{2}}-4 \sqrt[3]{x}

E

11+x2+1x\frac{1}{1+x^{2}}+\frac{1}{\sqrt{x}}

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