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Popular >

derivative of 4/3 pi*r^2

Solution

derivative of

\frac{4}{3} π \cdot r^{2}

Solution

\frac{8 π r}{3}

Solution steps

\frac{d}{d r} (\frac{4}{3} π r^{2})

Take the constant out:

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

= \frac{4}{3} π \frac{d}{d r} (r^{2})

Apply the Power Rule:

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

= \frac{4}{3} π 2 r^{2 - 1}

Simplify

\frac{4}{3} π 2 r^{2 - 1} : \frac{8 π r}{3}

= \frac{8 π r}{3}

Popular Examples

y^{''}-4y^'+5y=36cos(3t)-28sin(3t)

y^{^{''}} - 4 y^{^{'}} + 5 y = 36 cos (3 t) - 28 sin (3 t)

limit as x approaches 3 of 2x^2+5x-7

x \to 3 lim (2 x^{2} + 5 x - 7)

derivative of 1/2 cos^4(5x)

\frac{d}{d x} (\frac{1}{2} cos^{4} (5 x))

\frac{d}{d y} (1 - x^{2} y)

limit as n approaches infinity of 9

n \to \infty lim (9)

Frequently Asked Questions (FAQ)

What is the derivative of 4/3 pi*r^2 ?
The derivative of 4/3 pi*r^2 is (8pir)/3
What is the first derivative of 4/3 pi*r^2 ?
The first derivative of 4/3 pi*r^2 is (8pir)/3