Find the Derivative - d/dr 4/3*(pr^2)

Problem

d()/d(r)4/3*π*r^2

Solution

1. Identify the constant and the variable. In the expression 4/3*π*r^2 the term 4/3*π is a constant coefficient and r is the variable.

2. Apply the constant multiple rule, which allows the constant to be moved outside the derivative.

d()/d(r)4/3*π*r^2=4/3*πd(r^2)/d(r)

3. Apply the power rule for derivatives, d(r^n)/d(r)=n*r^(n−1) where n=2

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

4. Multiply the constant coefficient by the result of the derivative.

4/3*π⋅2*r=8/3*π*r

Final Answer

d()/d(r)4/3*π*r^2=8/3*π*r

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