derivative f(x)=(4x)/((x-9)^5)

解答

导数

f (x) = \frac{4 x}{( x - 9 ) ^{5}}

\frac{4 ( - 9 - 4 x )}{( x - 9 ) ^{6}}

求解步骤

\frac{d}{d x} (\frac{4 x}{( x - 9 ) ^{5}})

将常数提出:

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

= 4 \frac{d}{d x} (\frac{x}{( x - 9 ) ^{5}})

使用微分除法定则:

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

= 4 \cdot \frac{\frac{d x}{d x} ( x - 9 ) ^{5} - \frac{d}{d x} ( ( x - 9 ) ^{5} ) x}{( ( x - 9 ) ^{5} ) ^{2}}

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

\frac{d}{d x} ((x - 9)^{5}) = 5 (x - 9)^{4}

= 4 \cdot \frac{1 \cdot ( x - 9 ) ^{5} - 5 ( x - 9 ) ^{4} x}{( ( x - 9 ) ^{5} ) ^{2}}

化简

4 \cdot \frac{1 \cdot ( x - 9 ) ^{5} - 5 ( x - 9 ) ^{4} x}{( ( x - 9 ) ^{5} ) ^{2}} : \frac{4 ( - 9 - 4 x )}{( x - 9 ) ^{6}}

= \frac{4 ( - 9 - 4 x )}{( x - 9 ) ^{6}}

t a y l or ln (4 x), 1

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

\frac{\partial}{\partial x} (x y - x sin (y))

\frac{( t ^{2} + 1 ) ^{\frac{3}{2}}}{3}^{^{'}}

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