Find the Derivative of the Integral

Problem

d()/d(x)*(∫_^)(√(,x)*ln(x)*d(x))

Solution

1. Identify the operation required by the Fundamental Theorem of Calculus, which states that the derivative of an indefinite integral of a function is the function itself.

2. Apply the theorem to the expression d()/d(x)*(∫_^)(ƒ(x)*d(x))=ƒ(x)

3. Substitute the integrand ƒ(x)=√(,x)*ln(x) as the result of the differentiation.

Final Answer

d()/d(x)*(∫_^)(√(,x)*ln(x)*d(x))=√(,x)*ln(x)

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