Find the Derivative of the Integral integral of x^3 with respect to x

Problem

d()/d(x)*(∫_^)(x3*d(x))

Solution

1. Identify the operation as the derivative of an indefinite integral with respect to the same variable x

2. Apply the Fundamental Theorem of Calculus, which states that the derivative of an integral of a function ƒ(x) is the function ƒ(x) itself.

3. Simplify the expression by removing the integral and derivative operators, leaving the integrand.

Final Answer

d()/d(x)*(∫_^)(x3*d(x))=x3

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