Math Problem Statement

derivative of y=[5(x^1/2)(lnx)]/(tanx)

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Quotient Rule
Product Rule
Logarithmic Differentiation

Formulas

Quotient rule: (u/v)' = (u'v - uv')/v^2
Product rule: (fg)' = f'g + fg'
Derivative of sqrt(x): d/dx(sqrt(x)) = 1/(2sqrt(x))
Derivative of ln(x): d/dx(ln(x)) = 1/x
Derivative of tan(x): d/dx(tan(x)) = sec^2(x)

Theorems

Quotient Rule
Product Rule

Suitable Grade Level

Grades 11-12 (AP Calculus level)