Find the Derivative of the Integral

Problem

d()/d(x)*(∫_^)(√(,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 differentiation and integration are inverse operations.

3. Simplify the expression by recognizing that d()/d(x)*(∫_^)(ƒ(x)*d(x))=ƒ(x)

4. Evaluate the result by extracting the integrand √(,x)

Final Answer

d()/d(x)*(∫_^)(√(,x)*d(x))=√(,x)

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