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

Lösung

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

\frac{4 x ^{2} + 32 x + 3}{( x + 4 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{8 x ( x + 4 ) - 1 \cdot ( 4 x ^{2} - 3 )}{( x + 4 ) ^{2}} : \frac{4 x ^{2} + 32 x + 3}{( x + 4 ) ^{2}}

= \frac{4 x ^{2} + 32 x + 3}{( x + 4 ) ^{2}}

\frac{d}{d x} ((2 x + 8)^{2})

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