((x^3)/3)^'

Solution

(\frac{x ^{3}}{3})^{^{'}}

x^{2}

Solution steps

(\frac{x ^{3}}{3})^{'}

Take the constant out:

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

= \frac{1}{3} (x^{3})^{^{'}}

Apply the Power Rule:

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

= \frac{1}{3} \cdot 3 x^{3 - 1}

Simplify

\frac{1}{3} \cdot 3 x^{3 - 1} : x^{2}

= x^{2}

y^{^{'}} = (x + 1) (3 y - 1) 2

\frac{d}{d x} (\frac{8 x + x ^{2}}{( 4 + x ) ^{2}})

f (x) = 13 x^{3} (x^{2} - 3)

y = \frac{x}{81 + x ^{2}}, (0, 0)

\int \frac{14}{x ( x ^{2} + 25 )} d x