What is the derivative of sec - 1 ( x ) ?

rzepiowiffn

rzepiowiffn

Answered question

2023-03-14

What is the derivative of sec - 1 ( x ) ?

Answer & Explanation

kuskdtq

kuskdtq

Beginner2023-03-15Added 4 answers

Let y = sec - 1 x .
by rewriting in terms of secant,
sec y = x
by differentiating with respect to x,
sec y tan y y = 1
by dividing by sec y tan y,
y = 1 sec y tan y
since sec y = x and tan x = sec 2 y - 1 = x 2 - 1
y = 1 x x 2 - 1
Thus,
d d x ( sec - 1 x ) = 1 x x 2 - 1
Veronella6nk

Veronella6nk

Beginner2023-03-16Added 6 answers

Answer: ( sec - 1 ( x ) ) = 1 x x 2 - 1

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