Derivatives of sec(x) and csc(x) | Derivative rules | AP Calculus AB | Khan Academy

TL;DR

The video explains how to find the derivatives of secant and cosecant functions using the quotient rule.

Transcript

• [Voiceover] In a previous video we used the quotient rule in order to find the derivatives of tangent of x and cotangnet of x. And what I what to do in this video is to keep going and find the derivatives of secant of x and cosecant of x. So let's start with secant of x. The derivative with respect to x of secant of x. Well, secant of x is the sa... Read More

Key Insights

• ☺️ Secant x is equivalent to 1 over cosine x, and cosecant x is equivalent to 1 over sine x.
• ☺️ The quotient rule can be used to find the derivatives of both secant x and cosecant x.
• 😑 The derivatives can be expressed in terms of other trigonometric functions, such as tangent x, cotangent x, and secant x.

Summary & Key Takeaways

• The derivative of secant of x can be found by applying the quotient rule, resulting in sine x over cosine squared x.

• The derivative of cosecant of x can also be found using the quotient rule, giving negative cosine x over sine squared x.

• Both derivatives can also be expressed in terms of other trigonometric functions, with secant of x equal to tangent x times secant x, and cosecant of x equal to negative cotangent x times cosecant x.