derivative f(x)=(8x)/(e^x)

解答

导数

f (x) = \frac{8 x}{e ^{x}}

\frac{8 ( 1 - x )}{e ^{x}}

求解步骤

\frac{d}{d x} (\frac{8 x}{e ^{x}})

将常数提出:

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

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

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

\frac{d}{d x} (e^{x}) = e^{x}

= 8 \cdot \frac{1 \cdot e ^{x} - e ^{x} x}{( e ^{x} ) ^{2}}

化简

8 \cdot \frac{1 \cdot e ^{x} - e ^{x} x}{( e ^{x} ) ^{2}} : \frac{8 ( 1 - x )}{e ^{x}}

= \frac{8 ( 1 - x )}{e ^{x}}

\frac{d x}{d t} = 5 x (7 - x)

cos (x + y) d y = sin (x + y) d x

\int \frac{1}{( 625 + x ^{2} ) ^{\frac{3}{2}}} d x

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y^{3} - (10 x + 2) + 3 x y^{2} y^{^{'}} = 0