Vault Of Euclid

Derivative of Secant

Trigonometric and inverse trigonometric functions warmup

Show that \( \frac{d}{dx} (\sec x) = \sec x \tan x \).

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What you need first

Definition of secant and tangent in terms of sine and cosine
Derivative of cosine
The chain rule
The power rule for negative integers

What this problem tests

Tests the ability to apply the chain rule and use basic trigonometric identities to simplify expressions.

This is a standard derivation taught in introductory calculus courses when introducing the derivatives of trigonometric functions.

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