Vault Of Euclid

Derivative of Cosine via Sine

Trigonometric and inverse trigonometric functions warmup

Calculate \( \frac{d}{dx}(\cos x) \) from the known derivative of \( \sin x \).

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What you need first

the derivative of sine
the chain rule
trigonometric cofunction identities

What this problem tests

Tests the ability to combine trigonometric identities with the chain rule to derive new differentiation rules.

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

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