Find the Derivative - d/d@VAR f(x)=4/3pir^3

Problem

d()/d(r)4/3*π*r3

Solution

1. Identify the constant and the power of the variable r in the expression.

2. Apply the power rule for differentiation, which states that d(rn)/d(r)=n*r(n−1)

3. Multiply the constant coefficient 4/3*π by the exponent 3

4. Subtract 1 from the exponent of r to get the new power.

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

Final Answer

d()/d(r)4/3*π*r3=4*π*r2

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