(\partial)/(\partial x)((-18x)/((x-y)^4))

解答

\frac{\partial}{\partial x} (\frac{- 18 x}{( x - y ) ^{4}})

- \frac{18 ( - 3 x - y )}{( x - y ) ^{5}}

求解步骤

\frac{\partial}{\partial x} (\frac{- 18 x}{( x - y ) ^{4}})

化简

\frac{- 18 x}{( x - y ) ^{4}} : - \frac{18 x}{( x - y ) ^{4}}

= \frac{\partial}{\partial x} (- \frac{18 x}{( x - y ) ^{4}})

将

y

视为常数

将常数提出:

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

= - 18 \frac{\partial}{\partial x} (\frac{x}{( x - y ) ^{4}})

使用微分除法定则:

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

= - 18 \cdot \frac{\frac{\partial}{\partial x} ( x ) ( x - y ) ^{4} - \frac{\partial}{\partial x} ( ( x - y ) ^{4} ) x}{( ( x - y ) ^{4} ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} ((x - y)^{4}) = 4 (x - y)^{3}

= - 18 \cdot \frac{1 \cdot ( x - y ) ^{4} - 4 ( x - y ) ^{3} x}{( ( x - y ) ^{4} ) ^{2}}

化简

- 18 \cdot \frac{1 \cdot ( x - y ) ^{4} - 4 ( x - y ) ^{3} x}{( ( x - y ) ^{4} ) ^{2}} : - \frac{18 ( - 3 x - y )}{( x - y ) ^{5}}

= - \frac{18 ( - 3 x - y )}{( x - y ) ^{5}}

f (x) = \frac{100}{x ^{5}}

\frac{d}{d x} ((x - 1) ∣ x - 1 ∣)

\int_{1}^{4} 6 t ln (t) d t

\int sec (2 t) tan (2 t) d t

d er i v a t i v e (8 x - 6)^{2}