How do I differentiate y=tan(x) from the first principle?

Jete Igbodo 2022-07-19 Answered

Differentiate y= tanx using first principle 

 

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Answers (1)

Jeffrey Jordon
Answered 2022-11-07 Author has 2581 answers

1+tan2x=sec2x

tana+b=tana+tanb1-tanatanb

and

limx  0tanxx=1

Let f(x)=tanx

f(x)=lima0f(x+a)f(x)a

=lima0tan(x+a)tanxa

=lima0tanx+tanatanx+tan2xtanaa(1tanxtana)

=lima0tana(1+tan2x)a(1tanxtana)

=lima0tanasec2aa(1tanxtana)

Therefore

f'(x)=sec2x


 

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