How do you derive \(\displaystyle{y}={\tan{{x}}}\) using the

Bryant Jacobs

Bryant Jacobs

Answered question

2022-04-18

How do you derive y=tanx using the definition of the derivative?

Answer & Explanation

Jameson Jensen

Jameson Jensen

Beginner2022-04-19Added 16 answers

f(x)=tanx
f(x)=limh0tan(x+h)tanxh
=limh0tanx+tanh1tanxtanhtanxh
=limh0tanx+tanhtan+tan2xtanhh(1tanxtanh)
=limh0(tanhh1+tan2x1tanxtanh)
=(1)1+tan2x10=1+tan2x=sec2x

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