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Beliebt Rechnen >

derivative of (x+4/x)

Lösung

\frac{d}{d x} (\frac{x + 4}{x})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 4}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x + 4 ) x - \frac{d x}{d x} ( x + 4 )}{x ^{2}}

\frac{d}{d x} (x + 4) = 1

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of (x^3+ix^2+x+1/(x^2+i))

\frac{d}{d x} (\frac{x ^{3} + i x ^{2} + x + 1}{x ^{2} + i})

integral of (e^{7x})/(e^{7x)+8}

\int \frac{e ^{7 x}}{e ^{7 x} + 8} d x

integral of 1/((y-1)^{1/3)}

\int \frac{1}{( y - 1 ) ^{\frac{1}{3}}} d y

integral from 0 to 5 of 3x

\int_{0}^{5} 3 x d x

integral of e^x*x^2

\int e^{x} \cdot x^{2} d x