derivative ((2x+3))/((x^3-5))

Lösung

ableitung von

\frac{( 2 x + 3 )}{( x ^{3} - 5 )}

\frac{- 4 x ^{3} - 9 x ^{2} - 10}{( x ^{3} - 5 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

2 (x^{3} - 5) - 3 x^{2} (2 x + 3) : - 4 x^{3} - 9 x^{2} - 10

= \frac{- 4 x ^{3} - 9 x ^{2} - 10}{( x ^{3} - 5 ) ^{2}}

d er i v a t i v e 4 cos (4 x^{2})

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d er i v a t i v e e^{x^{2} + y^{2}}