Find the Derivative - d/dr k(R^2-r^2)

Problem

d()/d(r)*k*(R2−r2)

Solution

1. Distribute the constant k into the terms inside the parentheses to prepare for differentiation.

d()/d(r)*(k*R2−k*r2)

2. Apply the sum rule for derivatives, which allows for the differentiation of each term individually.

(d(k)*R2)/d(r)−(d(k)*r2)/d(r)

3. Identify constants in the expression. Since the derivative is with respect to r both k and R are treated as constants.

(d(k)*R2)/d(r)=0

4. Apply the power rule to the second term. The derivative of r2 with respect to r is 2*r

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

5. Combine the results and simplify the expression.

0−2*k*r=−2*k*r

Final Answer

d()/d(r)*k*(R2−r2)=−2*k*r

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