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

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

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Answer 1 · 2015-09-06T12:31:22

Use the tangent of a sum, continuity of tangent and $lim_(hrarr0)tan h/h = 1$

Explanation:

$f(x) = tanx$

$f'(x) = lim_(hrarr0)(tan(x+h) - tanx)/h$

$= lim_(hrarr0)((tanx+tan h)/(1-tanxtan h) - tanx)/h$

$= lim_(hrarr0)(tanx+tan h- tanx+tan^2xtan h)/(h(1-tanxtan h))$

$= lim_(hrarr0)(tan h/h * (1+tan^2x)/(1-tanxtan h))$

$= (1) * (1+tan^2x)/(1-0) = 1+tan^2x = sec^2x$

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

1 Answer

Explanation:

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