Vault Of Euclid

Derivative of the Square Root of Sine

Trigonometric and inverse trigonometric functions warmup

Find \( \frac{d}{dx}(\sqrt{\sin x}) \).

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What you need first

the chain rule
the power rule for derivatives
the derivative of the sine function
fractional and negative exponents

What this problem tests

Tests the ability to recognize a composite function, rewrite a radical as a fractional exponent, and correctly apply the chain rule.

This is a standard introductory calculus problem for practicing the chain rule with trigonometric functions.

More on Trigonometric and inverse trigonometric functions

Derivative of a Difference of Square Roots warmup
Equation of a Normal Line Using the Chain Rule warmup
Derivative of Nested Square Roots warmup
Derivative of a Composite Polynomial Function warmup

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