derivative of f(x)=-5/(x^(1/3)) — step-by-step solution

We save the definition:

f (x) = - \frac{5}{x^{\frac{1}{3}}}

To ease differentiation, the expression

- \frac{5}{x^{\frac{1}{3}}}

is turned into

-5 x^{- \frac{1}{3}}

Let's perform the differentiation:

\frac{d}{d x} (-5 x^{- \frac{1}{3}})

Apply the differentiation rule:

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

with f =

x

-5 \cdot (- \frac{1}{3} \cdot x^{(- \frac{1}{3} - 1)})

ℹ

-5 \cdot (- \frac{1}{3})

\frac{5}{3}

‖

- \frac{1}{3} - 1

\frac{- 1 - 1 \cdot 3}{3}

\frac{5}{3} \cdot x^{(\frac{- 1 - 1 \cdot 3}{3})}

ℹ

-1 \cdot 3

-3

‖

\frac{5}{3} \cdot x^{(\frac{- 1 - 3}{3})}

\frac{5 x^{(\frac{- 1 - 3}{3})}}{3}

\frac{5 x^{(\frac{- 1 - 3}{3})}}{3}

\frac{5 x^{- \frac{4}{3}}}{3}

\frac{5}{x^{\frac{4}{3}} \cdot 3}

▶Derivative:

\frac{5}{3 x^{\frac{4}{3}}}