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

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

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

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

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derivative of

V (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}

\frac{d y}{d t} = 3 t^{2} y + (4 t + 1) e^{t^{3}}

\frac{\partial}{\partial z} (sin (x z))

\int x^{2} x^{2} - 81 d x

\int_{0}^{4} (x^{2} - 3 x) d x

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