derivative (8x)/(7-cot(x))

解答

导数

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

\frac{8 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

求解步骤

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

将常数提出:

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

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

使用微分除法定则:

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

= 8 \cdot \frac{\frac{d x}{d x} ( 7 - cot ( x ) ) - \frac{d}{d x} ( 7 - cot ( x ) ) x}{( 7 - cot ( x ) ) ^{2}}

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

\frac{d}{d x} (7 - cot (x)) = csc^{2} (x)

= 8 \cdot \frac{1 \cdot ( 7 - cot ( x ) ) - csc ^{2} ( x ) x}{( 7 - cot ( x ) ) ^{2}}

化简

8 \cdot \frac{1 \cdot ( 7 - cot ( x ) ) - csc ^{2} ( x ) x}{( 7 - cot ( x ) ) ^{2}} : \frac{8 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

= \frac{8 ( 7 - cot ( x ) - x csc ^{2} ( x ) )}{( 7 - cot ( x ) ) ^{2}}

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