How do you find the derivative of (1-tan x)^2?

Jaslyn Gordon

Jaslyn Gordon

Answered question

2023-02-16

How to find the derivative of ( 1 - tan x ) 2 ?

Answer & Explanation

Roy Mcclain

Roy Mcclain

Beginner2023-02-17Added 9 answers

Derivative of ( 1 - tan x ) 2 is - 2 sec 2 x + 2 tan x sec 2 x
Explanation:
We can use Chain rule here. Let f ( x ) = ( 1 - tan x ) 2 . Then we can format it as
f ( g ( x ) ) = ( g ( x ) ) 2 , where g ( x ) = 1 - tan x .
Thus d f d x = d f d g × d g d x
2 × ( 1 - tan x ) × ( - sec 2 x )
Hence, - 2 sec 2 x + 2 tan x sec 2 x

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