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Beliebt Rechnen >

derivative y=(3+5x-8sqrt(x))/x

Lösung

ableitung von

y = \frac{3 + 5 x - 8 x}{x}

Lösung

\frac{4 x - 3}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 + 5 x - 8 x}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 + 5 x - 8 x ) x - \frac{d x}{d x} ( 3 + 5 x - 8 x )}{x ^{2}}

\frac{d}{d x} (3 + 5 x - 8 x) = - \frac{4}{x} + 5

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

= \frac{( - \frac{4}{x} + 5 ) x - 1 \cdot ( 3 + 5 x - 8 x )}{x ^{2}}

Vereinfache

\frac{( - \frac{4}{x} + 5 ) x - 1 \cdot ( 3 + 5 x - 8 x )}{x ^{2}} : \frac{4 x - 3}{x ^{2}}

= \frac{4 x - 3}{x ^{2}}

Graph

Beliebte Beispiele

derivative of (e^{3x}/(x^{15)})

\frac{d}{d x} (\frac{e ^{3 x}}{x ^{15}})

integral of (ln(9x))/x

\int \frac{ln ( 9 x )}{x} d x

integral of (1-x)(1-2x)(1-3x)

\int (1 - x) (1 - 2 x) (1 - 3 x) d x

integral of (x^8)/(x^9-2)

\int \frac{x ^{8}}{x ^{9} - 2} d x

integral from 0 to 5 of xe^{-x}

\int_{0}^{5} x e^{- x} d x