Math Problem Statement

Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] (Use non-identity functions for f(u) and g(x).) y = square root(x^3 + 9) (f(u), g(x)) = Find the derivative dy dx . dy dx

Solution

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Math Problem Analysis

Mathematical Concepts

Composite Functions
Chain Rule
Derivatives
Square Roots

Formulas

Chain Rule: dy/dx = f'(g(x)) * g'(x)
Derivative of square root function: f(u) = sqrt(u), f'(u) = 1/(2*sqrt(u))

Theorems

Chain Rule for derivatives

Suitable Grade Level

Grades 11-12