Vault Of Euclid

Derivative of the Tangent Function

Trigonometric and inverse trigonometric functions warmup

Derive the formula \( \frac{d}{dx} (\tan x) = \sec^2 x \).

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What you need first

The definition of tangent as sine over cosine
The definition of secant as one over cosine
The quotient rule for differentiation
The derivatives of sine and cosine
The Pythagorean trigonometric identity

What this problem tests

Tests the ability to apply the quotient rule and simplify trigonometric expressions using fundamental identities.

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

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