Derivative of Tangent Function/Corollary 2

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Corollary to Derivative of Tangent Function

$\dfrac \d {\d x} \tan x = 1 + \tan^2 x$


Proof

\(\ds \dfrac \d {\d x} \tan x\) \(=\) \(\ds \sec^2 x\) Derivative of $\tan x$
\(\ds \) \(=\) \(\ds 1 + \tan^2 x\) Difference of Squares of Secant and Tangent

$\blacksquare$


Sources