derivative f(x)=(2csc(x))/x

解答

导数

f (x) = \frac{2 csc ( x )}{x}

\frac{2 ( - x cot ( x ) csc ( x ) - csc ( x ) )}{x ^{2}}

求解步骤

\frac{d}{d x} (\frac{2 csc ( x )}{x})

将常数提出:

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

= 2 \frac{d}{d x} (\frac{csc ( x )}{x})

使用微分除法定则:

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

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

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

\frac{d x}{d x} = 1

= 2 \cdot \frac{( - cot ( x ) csc ( x ) ) x - 1 \cdot csc ( x )}{x ^{2}}

化简

2 \cdot \frac{( - cot ( x ) csc ( x ) ) x - 1 \cdot csc ( x )}{x ^{2}} : \frac{2 ( - x cot ( x ) csc ( x ) - csc ( x ) )}{x ^{2}}

= \frac{2 ( - x cot ( x ) csc ( x ) - csc ( x ) )}{x ^{2}}

\int_{6}^{7} \frac{1}{20} + \frac{x}{40} d x

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