derivative of sqrt(x/(3x^2+4))

Lösung

\frac{d}{d x} (\frac{x}{3 x ^{2} + 4})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{3 x ^{2} + 4})

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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