What is the derivative of ln(sec x)?

xafeguerpf3l

xafeguerpf3l

Answered question

2023-02-17

What is the derivative of ln ( sec x ) ?

Answer & Explanation

Quincy Doyle

Quincy Doyle

Beginner2023-02-18Added 8 answers

The chain rule can be applied here.
First, let's rename u = sec x and, consequently, ln(u) as our objective function.
Thus, remembering the chain rule statement:
d y d x = d y d u d u d x
Let's do it by parts:
d y d u = 1 u
and
d u d x = 1 sec x tan x
We can now aggregate them using the chain rule statement:
d y d x = 1 u sec x tan x = sec x tan x sec x = tan x

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