derivative of \sqrt[7]{x}-8/x

解答

\frac{d}{d x} (7 x - \frac{8}{x})

\frac{x ^{2} + 56 x ^{\frac{6}{7}}}{7 x ^{\frac{20}{7}}}

求解步骤

\frac{d}{d x} (7 x - \frac{8}{x})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (7 x) - \frac{d}{d x} (\frac{8}{x})

\frac{d}{d x} (7 x) = \frac{1}{7 x ^{\frac{6}{7}}}

\frac{d}{d x} (\frac{8}{x}) = - \frac{8}{x ^{2}}

= \frac{1}{7 x ^{\frac{6}{7}}} - (- \frac{8}{x ^{2}})

化简

\frac{1}{7 x ^{\frac{6}{7}}} - (- \frac{8}{x ^{2}}) : \frac{x ^{2} + 56 x ^{\frac{6}{7}}}{7 x ^{\frac{20}{7}}}

= \frac{x ^{2} + 56 x ^{\frac{6}{7}}}{7 x ^{\frac{20}{7}}}

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 y = 2 e^{x}

d er i v a t i v e y = x^{3 c o s (x)}

\int x^{5} d x

\int sec (t) (sec (t) - tan (t)) d t

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