Math Problem Statement

find the second order derivative of the function f(x)=xlnxf\left(x\right)=\sqrt{x}\ln x

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Product Rule
Quotient Rule
Logarithmic Functions

Formulas

Product rule: (u(x)v(x))' = u'(x)v(x) + u(x)v'(x)
Quotient rule: (f/g)' = (g*f' - f*g') / g^2
Derivative of ln(x): d/dx(ln(x)) = 1/x
Power rule: d/dx(x^n) = n*x^(n-1)

Theorems

Product Rule
Quotient Rule

Suitable Grade Level

College Calculus