derivative of (11-11x/(7x^{3/7)})

解答

\frac{d}{d x} (\frac{11 - 11 x}{7 x ^{\frac{3}{7}}})

\frac{- 44 x - 33}{49 x ^{\frac{10}{7}}}

求解步骤

\frac{d}{d x} (\frac{11 - 11 x}{7 x ^{\frac{3}{7}}})

将常数提出:

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

= \frac{1}{7} \frac{d}{d x} (\frac{11 - 11 x}{x ^{\frac{3}{7}}})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{7} \cdot \frac{\frac{d}{d x} ( 11 - 11 x ) x ^{\frac{3}{7}} - \frac{d}{d x} ( x ^{\frac{3}{7}} ) ( 11 - 11 x )}{( x ^{\frac{3}{7}} ) ^{2}}

\frac{d}{d x} (11 - 11 x) = - 11

\frac{d}{d x} (x^{\frac{3}{7}}) = \frac{3}{7 x ^{\frac{4}{7}}}

= \frac{1}{7} \cdot \frac{( - 11 ) x ^{\frac{3}{7}} - \frac{3}{7 x ^{\frac{4}{7}}} ( 11 - 11 x )}{( x ^{\frac{3}{7}} ) ^{2}}

化简

\frac{1}{7} \cdot \frac{( - 11 ) x ^{\frac{3}{7}} - \frac{3}{7 x ^{\frac{4}{7}}} ( 11 - 11 x )}{( x ^{\frac{3}{7}} ) ^{2}} : \frac{- 44 x - 33}{49 x ^{\frac{10}{7}}}

= \frac{- 44 x - 33}{49 x ^{\frac{10}{7}}}

\frac{\partial}{\partial v} (\frac{1}{v})

\frac{d}{d x} (3 x^{2} - 12 x + 5)

y \cdot d x + x^{2} \cdot d y = 0

\int \frac{2}{x} d x

\frac{d y}{d x} + y cos (x) = 2 cos (x)