Math Problem Statement
Given the function f, of, x, equals, start fraction, 3, x, cubed, divided by, 2, x, cubed, plus, 1, end fraction, commaf(x)= 2x 3 +1 3x 3
, find f, prime, of, xf ′ (x) in simplified form.
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Quotient Rule
Formulas
Quotient Rule: d/dx [u(x)/v(x)] = [u'(x)v(x) - u(x)v'(x)] / [v(x)]^2
Power Rule: d/dx [x^n] = n*x^(n-1)
Theorems
Quotient Rule
Simplification of Rational Expressions
Suitable Grade Level
Grades 11-12 or College-level Calculus