Derivative of Function of Constant Multiple/Examples/Secant of a x + b

Example of Derivative of Function of Constant Multiple

$\map {\dfrac \d {\d x} } {\map \sec {a x + b} } = a \map \sec {a x + b} \map \tan {a x + b}$

Proof

\(\ds \map {\dfrac \d {\d x} } {\map \sec {a x + b} }\)

\(=\)

\(\ds a \map {\dfrac \d {\map \d {a x + b} } } {\map \sec {a x + b} }\)

Derivative of Function of Constant Multiple: Corollary

\(\ds \)

\(=\)

\(\ds a \map \sec {a x + b} \map \tan {a x + b}\)

Derivative of Secant Function

$\blacksquare$

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Differentiation: Exercises $\text {IX}$: $20$.