derivative f(x)=(6x^5+4x)/(x^4+3)

Lösung

ableitung von

f (x) = \frac{6 x ^{5} + 4 x}{x ^{4} + 3}

\frac{6 x ^{8} + 78 x ^{4} + 12}{( x ^{4} + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 x ^{5} + 4 x}{x ^{4} + 3})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 6 x ^{5} + 4 x ) ( x ^{4} + 3 ) - \frac{d}{d x} ( x ^{4} + 3 ) ( 6 x ^{5} + 4 x )}{( x ^{4} + 3 ) ^{2}}

\frac{d}{d x} (6 x^{5} + 4 x) = 30 x^{4} + 4

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

= \frac{( 30 x ^{4} + 4 ) ( x ^{4} + 3 ) - 4 x ^{3} ( 6 x ^{5} + 4 x )}{( x ^{4} + 3 ) ^{2}}

Multipliziere aus

(30 x^{4} + 4) (x^{4} + 3) - 4 x^{3} (6 x^{5} + 4 x) : 6 x^{8} + 78 x^{4} + 12

= \frac{6 x ^{8} + 78 x ^{4} + 12}{( x ^{4} + 3 ) ^{2}}

\int (2 x - 3) d x

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