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Beliebt Rechnen >

derivative of x/((x^2+1^{1/2)}-1)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (1) = 0

= \frac{1}{( x ^{2} + 1 ) ^{\frac{3}{2}}} - 0

Vereinfache

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

Graph

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