derivative y=ln(2+x)+2/(2+x)

Lösung

ableitung von

y = ln (2 + x) + \frac{2}{2 + x}

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

Schritte zur Lösung

\frac{d}{d x} (ln (2 + x) + \frac{2}{2 + x})

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e 6 x - 1

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