derivative of ((0.9-0.4x)/x)

Lösung

\frac{d}{d x} (\frac{( 0.9 - 0.4 x )}{x})

- \frac{0.9}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( 0.9 - 0.4 x )}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 0.9 - 0.4 x ) x - \frac{d x}{d x} ( 0.9 - 0.4 x )}{x ^{2}}

\frac{d}{d x} (0.9 - 0.4 x) = - 0.4

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

= \frac{( - 0.4 ) x - 1 \cdot ( 0.9 - 0.4 x )}{x ^{2}}

Vereinfache

\frac{( - 0.4 ) x - 1 \cdot ( 0.9 - 0.4 x )}{x ^{2}} : - \frac{0.9}{x ^{2}}

= - \frac{0.9}{x ^{2}}

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