Find the Derivative - d/dr 312pr-6p^2r^2

Problem

d()/d(r)*(312*p*r−6*p2*r2)

Solution

1. Identify the variable of differentiation, which is r and treat p as a constant.

2. Apply the sum rule for derivatives to differentiate each term separately.

d()/d(r)*(312*p*r)−d()/d(r)*(6*p2*r2)

3. Apply the power rule to the first term, where the derivative of r is 1

d()/d(r)*(312*p*r)=312*p

4. Apply the power rule to the second term, where the derivative of r2 is 2*r

d()/d(r)*(6*p2*r2)=6*p2*(2*r)

5. Simplify the expression by multiplying the constants.

6*p2*(2*r)=12*p2*r

Final Answer

d()/d(r)*(312*p*r−6*p2*r2)=312*p−12*p2*r

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