Math Problem Statement
Given the function f, of, x, equals, minus, start fraction, 2, square root of, x, cubed, end square root, divided by, 5, end fraction, minus, 3, square root of, x, end square root, commaf(x)=−52x3−3x, find f, prime, of, 5, .f′(5). Express your answer as a single fraction in simplest radical form.
Solution
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Math Problem Analysis
Mathematical Concepts
Differentiation
Radical Functions
Fractional Exponents
Formulas
Power Rule: d/dx (x^n) = n*x^(n-1)
Derivative of √x: d/dx (√x) = 1/(2√x)
Simplification of Radicals
Theorems
Power Rule for Differentiation
Simplification of Radical Expressions
Suitable Grade Level
Grades 11-12 or Calculus I