What is the derivative of f(r)= 4/3 pir^3 ?

The derivative of f(r)= 4/3 pir^3 is 4pir^2

What is the first derivative of f(r)= 4/3 pir^3 ?

The first derivative of f(r)= 4/3 pir^3 is 4pir^2

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derivative of

f (r) = \frac{4}{3} π r^{3}

4 π r^{2}

Solution steps

\frac{d}{d r} (\frac{4}{3} π r^{3})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{4}{3} π \frac{d}{d r} (r^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{4}{3} π 3 r^{3 - 1}

Simplify

\frac{4}{3} π 3 r^{3 - 1} : 4 π r^{2}

= 4 π r^{2}

\int 3 y^{2} z + y e^{x} d x

\int t (t - 1)^{12} d t

\frac{\partial}{\partial x} (sin (5 x - 2 y))

\frac{\partial}{\partial x} (2 y e^{4 x^{2} - 6 y})

f (x) = - x

What is the derivative of f(r)= 4/3 pir^3 ?
The derivative of f(r)= 4/3 pir^3 is 4pir^2
What is the first derivative of f(r)= 4/3 pir^3 ?
The first derivative of f(r)= 4/3 pir^3 is 4pir^2