derivative (8x)/(5-cot(x))

解答

导数

\frac{8 x}{5 - cot ( x )}

\frac{8 ( 5 - cot ( x ) - x csc ^{2} ( x ) )}{( 5 - cot ( x ) ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{8 x}{5 - cot ( x )})

将常数提出:

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

= 8 \frac{d}{d x} (\frac{x}{5 - 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} ( 5 - cot ( x ) ) - \frac{d}{d x} ( 5 - cot ( x ) ) x}{( 5 - cot ( x ) ) ^{2}}

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

\frac{d}{d x} (5 - cot (x)) = csc^{2} (x)

= 8 \cdot \frac{1 \cdot ( 5 - cot ( x ) ) - csc ^{2} ( x ) x}{( 5 - cot ( x ) ) ^{2}}

化简

8 \cdot \frac{1 \cdot ( 5 - cot ( x ) ) - csc ^{2} ( x ) x}{( 5 - cot ( x ) ) ^{2}} : \frac{8 ( 5 - cot ( x ) - x csc ^{2} ( x ) )}{( 5 - cot ( x ) ) ^{2}}

= \frac{8 ( 5 - cot ( x ) - x csc ^{2} ( x ) )}{( 5 - cot ( x ) ) ^{2}}

\frac{d}{d x} (x arccos (\frac{1}{x}))

\int a e^{- b x} d x

\frac{d y}{d x} = y (1 - 0.0008 y)

\frac{d}{d x} (9 x + 7)

6 y^{^{''}} - 6 y^{^{'}} + 39 y = 0