What is the d/(dr)(4/3 pir^3) ?

The d/(dr)(4/3 pir^3) is 4pi{r}^2

What is the first d/(dr)(4/3 pir^3) ?

The first d/(dr)(4/3 pir^3) is 4pi{r}^2

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\frac{d}{d 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}

y = 2 x^{2} + 5 x + 1

f (x) = 2 lo g_{3} (x - 5)

f (x) = \frac{x ^{2} + 6 x}{2 x - 12}

y = x + \frac{4}{x}

1 - x^{2}