Find the Derivative of the Integral

Problem

d()/d(x)*(∫_^)(1/(x*ln(x))*d(x))

Solution

1. Identify the structure of the problem as the derivative of an indefinite integral.

2. Apply the Fundamental Theorem of Calculus, which states that the derivative of an indefinite integral of a function is the function itself.

3. Simplify the expression by removing the derivative and integral operators, leaving the integrand.

Final Answer

d()/d(x)*(∫_^)(1/(x*ln(x))*d(x))=1/(x*ln(x))

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