derivative x/(3sqrt(x^2+4))-1/4

Lösung

ableitung von

\frac{x}{3 x ^{2} + 4} - \frac{1}{4}

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (\frac{1}{4}) = 0

= \frac{4}{3 ( x ^{2} + 4 ) x ^{2} + 4} - 0

Vereinfache

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

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