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Beliebt Rechnen >

derivative y= 1/4 x^2-1/2 ln(x)

Lösung

ableitung von

y = \frac{1}{4} x^{2} - \frac{1}{2} ln (x)

Lösung

\frac{x}{2} - \frac{1}{2 x}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{4} x^{2} - \frac{1}{2} ln (x))

Vereinfache

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

= \frac{d}{d x} (\frac{x ^{2}}{4} - \frac{1}{2} ln (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x ^{2}}{4}) - \frac{d}{d x} (\frac{1}{2} ln (x))

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

\frac{d}{d x} (\frac{1}{2} ln (x)) = \frac{1}{2 x}

= \frac{x}{2} - \frac{1}{2 x}

Graph

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