derivative of sqrt((2x/(4x-3)))

Lösung

\frac{d}{d x} (\frac{2 x}{4 x - 3})

- \frac{3}{2 x ( 4 x - 3 ) ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x}{4 x - 3})

Wende die Kettenregel an:

\frac{1}{2 \frac{2 x}{4 x - 3}} \frac{d}{d x} (\frac{2 x}{4 x - 3})

= \frac{1}{2 \frac{2 x}{4 x - 3}} \frac{d}{d x} (\frac{2 x}{4 x - 3})

\frac{d}{d x} (\frac{2 x}{4 x - 3}) = - \frac{6}{( 4 x - 3 ) ^{2}}

= \frac{1}{2 \frac{2 x}{4 x - 3}} (- \frac{6}{( 4 x - 3 ) ^{2}})

Vereinfache

\frac{1}{2 \frac{2 x}{4 x - 3}} (- \frac{6}{( 4 x - 3 ) ^{2}}) : - \frac{3}{2 x ( 4 x - 3 ) ^{\frac{3}{2}}}

= - \frac{3}{2 x ( 4 x - 3 ) ^{\frac{3}{2}}}

\int 13 x^{3} d x

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