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Beliebt Rechnen >

derivative of x/({f(x)})

Lösung

\frac{d}{d x} (\frac{x}{f ( x )})

Lösung

\frac{f ( x ) - x \frac{d}{d x} ( f ( x ) )}{f ( x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{f ( x )})

Wende die Quotientenregel an:

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

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

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

= \frac{1 \cdot f ( x ) - \frac{d}{d x} ( f ( x ) ) x}{f ( x ) ^{2}}

Vereinfache

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

Beliebte Beispiele

2yy^'-xy^'=y-2x

2 y y^{^{'}} - x y^{^{'}} = y - 2 x

integral of (2ysin(x)-x^3+ln(y))

\int (2 y sin (x) - x^{3} + ln (y)) d y

y^{''}-9y^'=81t

y^{^{''}} - 9 y^{^{'}} = 81 t

derivative of (arccos(x)/x)

\frac{d}{d x} (\frac{arccos ( x )}{x})

derivative of tan(x+1/(x^2))

\frac{d}{d x} (tan (x) + \frac{1}{x ^{2}})