derivative f(x)=sqrt(x/(x+7))

Lösung

ableitung von

f (x) = \frac{x}{x + 7}

\frac{7}{2 x ( x + 7 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{x + 7})

Wende die Kettenregel an:

\frac{1}{2 \frac{x}{x + 7}} \frac{d}{d x} (\frac{x}{x + 7})

= \frac{1}{2 \frac{x}{x + 7}} \frac{d}{d x} (\frac{x}{x + 7})

\frac{d}{d x} (\frac{x}{x + 7}) = \frac{7}{( x + 7 ) ^{2}}

= \frac{1}{2 \frac{x}{x + 7}} \cdot \frac{7}{( x + 7 ) ^{2}}

Vereinfache

\frac{1}{2 \frac{x}{x + 7}} \cdot \frac{7}{( x + 7 ) ^{2}} : \frac{7}{2 x ( x + 7 ) ^{\frac{3}{2}}}

= \frac{7}{2 x ( x + 7 ) ^{\frac{3}{2}}}

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