Derivative of Tangent Function/Corollary 2

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

• 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $5$. Differential Calculus: Appendix: Derivatives of fundamental functions: $3.$ Trigonometric functions