What is the derivative of 1/(6x^{5/6}) ?

The derivative of 1/(6x^{5/6}) is -5/(36x^{11/6)}

What is the first derivative of 1/(6x^{5/6}) ?

The first derivative of 1/(6x^{5/6}) is -5/(36x^{11/6)}

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{6} (- \frac{5}{6} x^{- \frac{5}{6} - 1}) : - \frac{5}{36 x ^{\frac{11}{6}}}

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

(1, 1), (4, - \frac{1}{2})

\frac{\partial}{\partial x} (r)

y = \frac{- 8 x}{x ^{2} + 1}, (- 1, 4)

x^{2} (240 - \frac{x}{3})

\frac{1}{2} x^{4} - 8

What is the derivative of 1/(6x^{5/6}) ?
The derivative of 1/(6x^{5/6}) is -5/(36x^{11/6)}
What is the first derivative of 1/(6x^{5/6}) ?
The first derivative of 1/(6x^{5/6}) is -5/(36x^{11/6)}