derivative of (sqrt(x+5)/(sqrt(x+2)))

Lösung

\frac{d}{d x} (\frac{x + 5}{x + 2})

- \frac{3}{2 x + 5 ( x + 2 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 5}{x + 2})

Vereinfache

\frac{x + 5}{x + 2} : \frac{x + 5}{x + 2}

= \frac{d}{d x} (\frac{x + 5}{x + 2})

Wende die Kettenregel an:

\frac{1}{2 \frac{x + 5}{x + 2}} \frac{d}{d x} (\frac{x + 5}{x + 2})

= \frac{1}{2 \frac{x + 5}{x + 2}} \frac{d}{d x} (\frac{x + 5}{x + 2})

\frac{d}{d x} (\frac{x + 5}{x + 2}) = - \frac{3}{( x + 2 ) ^{2}}

= \frac{1}{2 \frac{x + 5}{x + 2}} (- \frac{3}{( x + 2 ) ^{2}})

Vereinfache

\frac{1}{2 \frac{x + 5}{x + 2}} (- \frac{3}{( x + 2 ) ^{2}}) : - \frac{3}{2 x + 5 ( x + 2 ) ^{\frac{3}{2}}}

= - \frac{3}{2 x + 5 ( x + 2 ) ^{\frac{3}{2}}}

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