Derivative of Tangent Function/Corollary 3
Jump to navigation
Jump to search
Corollary to Derivative of Tangent Function
- $\map {\dfrac \d {\d x} } {\tan a x} = a \paren {\tan^2 a x + 1}$
Proof
\(\ds \map {\dfrac \d {\d x} } {\tan x}\) | \(=\) | \(\ds \sec^2 x\) | Derivative of $\tan x$ | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \map {\dfrac \d {\d x} } {\tan a x}\) | \(=\) | \(\ds a \sec^2 a x\) | Derivative of Function of Constant Multiple | ||||||||||
\(\ds \) | \(=\) | \(\ds a \paren {\tan^2 a x + 1}\) | Difference of Squares of Secant and Tangent |
$\blacksquare$