Find the Derivative of the Integral

Problem

d()/d(x)*(∫_0^6)(√(,36−x2)*d(x))

Solution

1. Identify the nature of the expression. The expression is a definite integral with constant limits of integration, 0 and 6

2. Recognize that a definite integral with constant limits results in a constant value (a real number).

3. Apply the constant rule for differentiation. The derivative of any constant with respect to x is 0

4. Conclude that since the integral represents a fixed area (specifically, the area of a quarter-circle of radius 6, its derivative with respect to x is zero.

Final Answer

d()/d(x)*(∫_0^6)(√(,36−x2)*d(x))=0

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