Find the derivative of a function containing nested square roots using the chain rule.

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Derivative of Nested Square Roots

The chain rule warmup

Find the derivative of \( f(x) = \sqrt{4-\sqrt{4+x}} \).

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What you need first

the power rule for derivatives
the chain rule
converting between radical and fractional exponent notation

What this problem tests

Tests the ability to recognize nested functions, rewrite radicals as fractional exponents, and apply the chain rule systematically without losing track of the layers.

This is a standard Calculus I problem designed to test repeated application of the chain rule.

Derivative of Nested Square Roots

What you need first

What this problem tests

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