derivative sqrt((x+3)/(x-3))

Lösung

ableitung von

\frac{x + 3}{x - 3}

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 3}{x - 3})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x + 3}{x - 3}) = - \frac{6}{( x - 3 ) ^{2}}

= \frac{1}{2 \frac{x + 3}{x - 3}} (- \frac{6}{( x - 3 ) ^{2}})

Vereinfache

\frac{1}{2 \frac{x + 3}{x - 3}} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{3}{x + 3 ( x - 3 ) ^{\frac{3}{2}}}

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

\frac{\partial}{\partial y} (4 x + y)

l a pl a ce t r an s f or m 7 t^{3}

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