Math Problem Statement
Given the function f, of, x, equals, minus, start fraction, square root of, x, end square root, divided by, 5, end fraction, plus, start fraction, 5, square root of, x, cubed, end square root, divided by, 6, end fraction, commaf(x)=− 5 x
+ 6 5 x 3
, find f, prime, of, 4, .f ′ (4). Express your answer as a single fraction in simplest form.
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Exponent Rules
Square Roots
Formulas
Power Rule: d/dx (x^n) = n*x^(n-1)
Fractional Exponents: √x = x^(1/2), √x^3 = x^(3/2)
Theorems
Power Rule for Differentiation
Suitable Grade Level
Grades 11-12 (High School Calculus)