Find the derivative of the function f by using the rules of differentiation.
f(r)=4/3ðr^3
To find the derivative of the function f(r) = (4/3)πr³, we can use the power rule for differentiation.
The power rule states that if we have a term of the form f(x) = Axⁿ, where A is a constant and n is a real number, then the derivative of f(x) is given by f'(x) = nAxⁿ⁻¹.
In our case, f(r) = (4/3)πr³, where A = (4/3)π and n = 3. Applying the power rule, we differentiate each term:
f'(r) = (3)(4/3)πr^(3-1)
= (4π)r²
= 4πr²
Therefore, the derivative of f(r) = (4/3)πr³ is f'(r) = 4πr².