Find the Derivative - d/dr V(r)=4/3*(pr^3)

Problem

d()/d(r)*V(r)=4/3*π*r3

Solution

1. Identify the constant and the variable in the expression. Here, 4/3*π is a constant coefficient and r is the variable.

2. Apply the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of the function.

3. Apply the power rule to the term r3 The power rule states that d(rn)/d(r)=n*r(n−1)

4. Multiply the constant coefficient by the result of the power rule.

V(r)′=4/3*π⋅3*r(3−1)

5. Simplify the expression by canceling the 3 in the numerator and denominator and subtracting the exponents.

V(r)′=4*π*r2

Final Answer

d()/d(r)4/3*π*r3=4*π*r2

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