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

Problem

d()/d(r)4/3*π*r3

Solution

1. Identify the constant and the power of the variable r The expression is a constant 4/3*π multiplied by r3

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.

d()/d(r)4/3*π*r3=4/3*πd(r3)/d(r)

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

d(r3)/d(r)=3*r(3−1)

4. Simplify the expression by performing the subtraction in the exponent.

d(r3)/d(r)=3*r2

5. Multiply the constant back into the result.

4/3*π⋅3*r2=4*π*r2

Final Answer

d()/d(r)4/3*π*r3=4*π*r2

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