What is the derivative of tan(x^2)?

Heath Frazier

Heath Frazier

Answered question

2023-02-13

What is the derivative of tan ( x 2 ) ?

Answer & Explanation

Lyric Yates

Lyric Yates

Beginner2023-02-14Added 3 answers

Step 1
y = tan ( x 2 ) = tan ( u )
d y d u = sec 2 ( u ) = sec 2 ( x 2 )
u = x 2 , d u d x = 2 x
Step 2
Apply the chain rule:
d y d u d u d x = 2 x sec 2 ( x 2 ) = d y d x
Remember that:
If y = tan x , d y d x = sec 2 ( x )
It's a general rule.

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