Find the Derivative - d/dr (d^2)/(dr^2)*(pr^2)

Problem

d()/d(r)d2()/(d(r)2)*(p*r2)

Solution

1. Identify the expression to be differentiated. The task requires finding the third derivative of p*r2 with respect to r which is written as d()/d(r)*(d2()/(d(r)2)*(p*r2))

2. Calculate the first derivative of p*r2 with respect to r using the power rule, treating p as a constant.

(d(p)*r2)/d(r)=2*p*r

3. Calculate the second derivative by differentiating the result of the first derivative.

(d(2)*p*r)/d(r)=2*p

4. Calculate the third derivative by differentiating the result of the second derivative. Since 2*p is a constant with respect to r its derivative is zero.

(d(2)*p)/d(r)=0

Final Answer

d()/d(r)d2()/(d(r)2)*(p*r2)=0

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