Find the derivative of a function involving square roots by first simplifying the expression using exponent rules.

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Derivative of a Difference of Square Roots

The chain rule warmup

Find the derivative of \( \sqrt{\frac{4}{x}} - \sqrt{3x} \).

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What you need first

Properties of exponents and radicals
The power rule for differentiation
The difference rule for differentiation

What this problem tests

Tests the ability to rewrite radical and rational expressions using exponent rules and to apply the power rule for differentiation.

This problem is typical of early calculus exercises where students learn to simplify expressions algebraically before differentiating, to avoid unnecessarily complicated applications of the chain rule or quotient rule.

Derivative of a Difference of Square Roots

What you need first

What this problem tests

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