Math Problem Statement
Find the first and second derivatives of the function.
f(x) =
x2
7 + 4x
f ′(x)
=
14x+4x2(7+4x)2 f ″(x)
=
(7+4x2)(14+8x)−(14x+4x2)(8(7+4x))(7+4x)4
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Quotient Rule
Higher-Order Derivatives
Formulas
Quotient Rule: d/dx [u(x) / v(x)] = [u'(x)v(x) - u(x)v'(x)] / [v(x)]^2
First Derivative of f(x): f'(x) = (4x^2 + 14x) / (7 + 4x)^2
Second Derivative of f(x): f''(x) = [(7 + 4x)(8x + 14) - (4x^2 + 14x)(8)] / (7 + 4x)^3
Theorems
Quotient Rule
Suitable Grade Level
Undergraduate Calculus
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