Find the Derivative of the Integral integral of sin(x) with respect to x

Problem

d()/d(x)*(∫_^)(sin(x)*d(x))

Solution

1. Identify the operation as the derivative of an indefinite integral.

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

3. Recognize that d()/d(x)*(∫_^)(ƒ(x)*d(x))=ƒ(x)

4. Substitute ƒ(x)=sin(x) into the theorem.

Final Answer

d()/d(x)*(∫_^)(sin(x)*d(x))=sin(x)

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