Multiply (d^2)/(dr^2)*(pir^2)

Problem

d2()/(d(r)2)*(π*r2)

Solution

1. Identify the expression as the second derivative of the area of a circle with respect to its radius r

2. Apply the constant multiple rule to move the constant π outside of the differentiation operator.

πd2()/(d(r)2)*r2

3. Find the first derivative of r2 using the power rule, where d(rn)/d(r)=n*r(n−1)

πd()/d(r)*(2*r)

4. Find the second derivative by differentiating 2*r with respect to r

π*(2)

5. Simplify the final expression by multiplying the constants.

2*π

Final Answer

d2()/(d(r)2)*π*r2=2*π

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