Find the Derivative of the Integral

Problem

d()/d(x)*(∫_^)(sin(√(,x))/√(,x)*d(x))

Solution

1. Identify the operation required, which is to find 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. Recognize that d()/d(x)*(∫_^)(ƒ(x)*d(x))=ƒ(x)

4. Substitute the integrand ƒ(x)=sin(√(,x))/√(,x) as the result.

Final Answer

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

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