derivative w/(w+c/w)

Lösung

ableitung von

\frac{w}{w + \frac{c}{w}}

\frac{2 c w}{( w ^{2} + c ) ^{2}}

Schritte zur Lösung

\frac{d}{d w} (\frac{w}{w + \frac{c}{w}})

Wende die Quotientenregel an:

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

= \frac{\frac{d w}{d w} ( w + \frac{c}{w} ) - \frac{d}{d w} ( w + \frac{c}{w} ) w}{( w + \frac{c}{w} ) ^{2}}

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

\frac{d}{d w} (w + \frac{c}{w}) = 1 - \frac{c}{w ^{2}}

= \frac{1 \cdot ( w + \frac{c}{w} ) - ( 1 - \frac{c}{w ^{2}} ) w}{( w + \frac{c}{w} ) ^{2}}

Vereinfache

\frac{1 \cdot ( w + \frac{c}{w} ) - ( 1 - \frac{c}{w ^{2}} ) w}{( w + \frac{c}{w} ) ^{2}} : \frac{2 c w}{( w ^{2} + c ) ^{2}}

= \frac{2 c w}{( w ^{2} + c ) ^{2}}

t an g e n t y = x^{2} - 6, at x = a

d er i v a t i v e \frac{x ^{2} - 4}{x - 3}

s l o p e f (x) = 18 x^{3} - x

\frac{\partial}{\partial x} (5 tan (5 x))

\frac{d}{d x} (\frac{cos ( 2 x )}{sin ( 2 x )})