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

Problem

d()/d(x)*(∫_^)(tan(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)

Final Answer

d()/d(x)*(∫_^)(tan(x)*d(x))=tan(x)

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