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

The first (4/3 pir^3)^' is 4pir^2

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(4/3 pir^3)^'

(\frac{4}{3} π r^{3})^{^{'}}

4 π r^{2}

Solution steps

(\frac{4}{3} π r^{3})^{'}

Take the constant out:

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

= \frac{4}{3} π (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 - (x - 1)^{2} d x

f (x) = x^{2} e^{6 x}

\frac{d}{d x} (cos (x) - 4 tan (x))

\frac{d}{d x} (x arctan (x))

2 y^{^{''}} - y^{^{'}} + 3 y = 0