derivative ((2x^4+5x^3-2x-8))/((x+3))

Lösung

ableitung von

\frac{( 2 x ^{4} + 5 x ^{3} - 2 x - 8 )}{( x + 3 )}

\frac{6 x ^{4} + 34 x ^{3} + 45 x ^{2} + 2}{( x + 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{4} + 5 x ^{3} - 2 x - 8}{x + 3})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 2 x ^{4} + 5 x ^{3} - 2 x - 8 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( 2 x ^{4} + 5 x ^{3} - 2 x - 8 )}{( x + 3 ) ^{2}}

\frac{d}{d x} (2 x^{4} + 5 x^{3} - 2 x - 8) = 8 x^{3} + 15 x^{2} - 2

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

= \frac{( 8 x ^{3} + 15 x ^{2} - 2 ) ( x + 3 ) - 1 \cdot ( 2 x ^{4} + 5 x ^{3} - 2 x - 8 )}{( x + 3 ) ^{2}}

Vereinfache

\frac{( 8 x ^{3} + 15 x ^{2} - 2 ) ( x + 3 ) - 1 \cdot ( 2 x ^{4} + 5 x ^{3} - 2 x - 8 )}{( x + 3 ) ^{2}} : \frac{6 x ^{4} + 34 x ^{3} + 45 x ^{2} + 2}{( x + 3 ) ^{2}}

= \frac{6 x ^{4} + 34 x ^{3} + 45 x ^{2} + 2}{( x + 3 ) ^{2}}