derivative (6e^w)/(7w)

解答

导数

\frac{6 e ^{w}}{7 w}

\frac{6 ( e ^{w} w - e ^{w} )}{7 w ^{2}}

求解步骤

\frac{d}{d w} (\frac{6 e ^{w}}{7 w})

将常数提出:

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

= \frac{6}{7} \frac{d}{d w} (\frac{e ^{w}}{w})

使用微分除法定则:

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

= \frac{6}{7} \cdot \frac{\frac{d}{d w} ( e ^{w} ) w - \frac{d w}{d w} e ^{w}}{w ^{2}}

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

\frac{d w}{d w} = 1

= \frac{6}{7} \cdot \frac{e ^{w} w - 1 \cdot e ^{w}}{w ^{2}}

化简

\frac{6}{7} \cdot \frac{e ^{w} w - 1 \cdot e ^{w}}{w ^{2}} : \frac{6 ( e ^{w} w - e ^{w} )}{7 w ^{2}}

= \frac{6 ( e ^{w} w - e ^{w} )}{7 w ^{2}}

\frac{d}{d x} (1 4^{2 x})

d er i v a t i v e \frac{5 u}{4 u ^{2} + 1}

t an g e n t f (x) = x + 2, at x = 2

t a y l or 3 1 + x, 0

t an g e n t x^{3} + x^{2} + \frac{6}{x}