derivative of 1/(6x^{5/6}) — step-by-step solution

⚠ 6x is read as the product 6*x: for a power, write 6^x

⚠ 1/(6x^{5/6}) is read as 1/(6x^(5/6))

To simplify differentiation, we rewrite

\frac{1}{6 x^{\frac{5}{6}}}

\frac{1}{6} \cdot x^{- \frac{5}{6}}

Let's perform the differentiation:

\frac{d}{d x} (\frac{1}{6} \cdot x^{- \frac{5}{6}})

We differentiate using:

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

(where f =

x

)

\frac{1}{6} \cdot (- \frac{5}{6} \cdot x^{(- \frac{5}{6} - 1)})

ℹ

\frac{1}{6} \cdot (- \frac{5}{6})

- \frac{5}{36}

‖

- \frac{5}{6} - 1

\frac{- 5 - 1 \cdot 6}{6}

- \frac{5}{36} \cdot x^{(\frac{- 5 - 1 \cdot 6}{6})}

- \frac{5}{36} \cdot x^{(\frac{- 5 - 6}{6})}

ℹ

- \frac{5}{36} \cdot x^{(\frac{- 5 - 6}{6})}

- \frac{5 x^{(\frac{- 5 - 6}{6})}}{36}

‖

- 5 - 6

-11

- \frac{5 x^{- \frac{11}{6}}}{36}

- \frac{5}{x^{\frac{11}{6}} \cdot 36}

▶Derivative:

- \frac{5}{36 x^{\frac{11}{6}}}