Math Problem Statement
Solution
To differentiate each of these functions, we'll use various rules of differentiation such as the product rule, quotient rule, and trigonometric identities. Here are the derivatives:
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( f(x) = \frac{\sqrt{x} + 2x}{7x -
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Math Problem Analysis
Mathematical Concepts
Differentiation
Quotient Rule
Product Rule
Trigonometric Differentiation
Formulas
Quotient Rule: (u/v)' = (u'v - uv')/v^2
Product Rule: (uv)' = u'v + uv'
Trigonometric Derivatives: d/dx(sin x) = cos x, d/dx(cos x) = -sin x, d/dx(tan x) = sec^2 x, d/dx(sec x) = sec x tan x
Theorems
Fundamental rules of differentiation
Suitable Grade Level
Grades 11-12
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