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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (sin (\frac{x}{( y + 1 )}))

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d er i v a t i v e (e^{x})^{2} + 2 ln (x^{e})