Derivative of Cosine Squared
Trigonometric and inverse trigonometric functions
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Calculate \(\frac{d}{dx}(\cos^2 x)\).
calculus-iderivativeschain-ruletrigonometric-functionscosinesinedouble-angle-identityevaluate-derivativecomposite-functionspower-rule
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What you need first
- The power rule for derivatives
- The chain rule
- The derivative of the cosine function
- Trigonometric identities, specifically the double-angle formula for sine
What this problem tests
Tests the ability to recognize a composite function involving trigonometry and correctly apply the chain rule, as well as simplifying the result using basic trigonometric identities.
This is a fundamental exercise in a first-semester Calculus course, introducing the application of the chain rule to trigonometric functions.
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