derivative of 1/(6x^{5/6})

해법

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

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

솔루션 단계

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

정수를 빼라:

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

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

지수 규칙 적용:

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

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

전원 규칙을 적용합니다:

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

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

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

간소화하다 :

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

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