Worksheet: Derivatives of Inverse Trigonometric Functions

In this worksheet, we will practice finding the derivatives of the inverses of trigonometric functions.

Q1:

Find d d s i n 𝑥 𝑥 1 .

  • A 1 1 + 𝑥 2
  • B 1 1 𝑥 2 , where 1 < 𝑥 < 1
  • C 1 1 + 𝑥 2
  • D 1 1 𝑥 2 , where 1 < 𝑥 < 1
  • E 1 1 + 𝑥 2

Q2:

Find d d s i n 𝑥 𝑥 𝑎 1 , where 𝑎 0 .

  • A 1 𝑎 + 𝑥 2 2
  • B 1 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 |
  • C 1 𝑎 + 𝑥 2 2
  • D 1 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 |
  • E 𝑎 𝑎 + 𝑥 2 2

Q3:

Find d d c s c 𝑥 𝑥 𝑎 1 .

  • A 𝑎 𝑥 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 | and 𝑥 0
  • B 𝑎 | 𝑥 | 𝑥 𝑎 2 2 , where | 𝑥 | > | 𝑎 |
  • C 𝑎 𝑥 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 | and 𝑥 0
  • D 𝑎 | 𝑥 | 𝑥 𝑎 2 2 , where | 𝑥 | > | 𝑎 |
  • E 1 𝑥 𝑥 𝑎 2 2 , where | 𝑥 | > | 𝑎 |

Q4:

Find d d c s c 𝑥 𝑥 1 .

  • A 1 𝑥 1 𝑥 2 , where 1 < 𝑥 < 1 and 𝑥 0
  • B 1 | 𝑥 | 𝑥 1 2 , where | 𝑥 | > 1
  • C 1 𝑥 1 𝑥 2 , where 1 < 𝑥 < 1 and 𝑥 0
  • D 1 | 𝑥 | 𝑥 1 2 , where | 𝑥 | > 1
  • E 1 𝑥 𝑥 1 2 , where | 𝑥 | > 1

Q5:

Find d d s e c 𝑥 𝑥 𝑎 1 , where 𝑎 0 .

  • A 𝑎 𝑥 𝑎 𝑥 2 2 , where 𝑥 < | 𝑎 | and 𝑥 0
  • B 𝑎 | 𝑥 | 𝑥 𝑎 2 2 , where | 𝑥 | > | 𝑎 |
  • C 𝑎 𝑥 𝑎 𝑥 2 2 , where 𝑥 < | 𝑎 | and 𝑥 0
  • D 𝑎 | 𝑥 | 𝑥 𝑎 2 2 , where | 𝑥 | > | 𝑎 |
  • E 𝑎 𝑥 𝑥 𝑎 2 2 , where | 𝑥 | > | 𝑎 |

Q6:

Find d d s e c 𝑥 𝑥 .

  • A 1 𝑥 1 𝑥 , where 1 < 𝑥 < 1 and 𝑥 0
  • B 1 | 𝑥 | 𝑥 1 , where | 𝑥 | > 1
  • C 1 𝑥 1 𝑥 , where 1 < 𝑥 < 1 and 𝑥 0
  • D 1 | 𝑥 | 𝑥 1 , where | 𝑥 | > 1
  • E 1 𝑥 𝑥 1 , where | 𝑥 | > 1

Q7:

Find d d c o t 𝑥 𝑥 𝑎 1 , where 𝑎 0 .

  • A 𝑎 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 |
  • B 𝑎 𝑎 + 𝑥 2 2
  • C 𝑎 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 |
  • D 𝑎 𝑎 + 𝑥 2 2
  • E 1 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 |

Q8:

Find d d c o t 𝑥 𝑥 1 .

  • A 1 1 𝑥 2 , where 1 < 𝑥 < 1
  • B 1 1 + 𝑥 2
  • C 1 1 𝑥 2 , where 1 < 𝑥 < 1
  • D 1 1 + 𝑥 2
  • E 1 1 𝑥 2 , where 1 < 𝑥 < 1

Q9:

Find d d t a n 𝑥 𝑥 𝑎 1 , where 𝑎 0 .

  • A 𝑎 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 |
  • B 𝑎 𝑎 + 𝑥 2 2
  • C 𝑎 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 |
  • D 𝑎 𝑎 + 𝑥 2 2
  • E 1 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 |

Q10:

Find d d t a n 𝑥 𝑥 1 .

  • A 1 1 𝑥 2 , where 1 < 𝑥 < 1
  • B 1 1 + 𝑥 2
  • C 1 1 𝑥 2 , where 1 < 𝑥 < 1
  • D 1 1 + 𝑥 2
  • E 1 1 𝑥 2 , where 1 < 𝑥 < 1

Q11:

Find d d c o s 𝑥 𝑥 𝑎 1 , where 𝑎 0 .

  • A 1 𝑎 + 𝑥 2 2
  • B 1 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 |
  • C 1 𝑎 + 𝑥 2 2
  • D 1 𝑎 𝑥 2 2 , where | 𝑥 | < | 𝑎 |
  • E 𝑎 𝑎 + 𝑥 2 2

Q12:

Find d d c o s 𝑥 𝑥 1 .

  • A 1 1 + 𝑥 2
  • B 1 1 𝑥 2 , where 1 < 𝑥 < 1
  • C 1 1 + 𝑥 2
  • D 1 1 𝑥 2 , where 1 < 𝑥 < 1
  • E 1 1 + 𝑥 2

Q13:

Given that 4 𝑥 𝑦 = 3 𝑥 5 𝑥 𝑦 t a n , find d d 𝑦 𝑥 by implicit differentiation.

  • A d d 𝑦 𝑥 = 3 + 3 𝑥 𝑦 5 𝑦 5 𝑥 𝑦 8 𝑥 𝑦 4 𝑥 1 0 𝑥 𝑦 1 0 𝑥 𝑦
  • B d d 𝑦 𝑥 = 3 + 3 𝑥 𝑦 5 𝑦 5 𝑥 𝑦 + 4 𝑥 𝑦 1 0 𝑥 𝑦 + 1 0 𝑥 𝑦
  • C d d 𝑦 𝑥 = 3 3 𝑥 𝑦 5 𝑦 5 𝑥 𝑦 8 𝑥 𝑦 4 𝑥 1 0 𝑥 𝑦 + 1 0 𝑥 𝑦
  • D d d 𝑦 𝑥 = 3 + 3 𝑥 𝑦 5 𝑦 5 𝑥 𝑦 8 𝑥 𝑦 4 𝑥 + 1 0 𝑥 𝑦 + 1 0 𝑥 𝑦
  • E d d 𝑦 𝑥 = 3 + 3 𝑥 𝑦 5 𝑦 5 𝑥 𝑦 8 𝑥 𝑦 4 𝑥 + 5 𝑥 𝑦 + 5 𝑥 𝑦

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.