derivative ((x^2+x-17))/((x-4))

Lösung

ableitung von

\frac{( x ^{2} + x - 17 )}{( x - 4 )}

\frac{x ^{2} - 8 x + 13}{( x - 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + x - 17}{x - 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} + x - 17 ) ( x - 4 ) - \frac{d}{d x} ( x - 4 ) ( x ^{2} + x - 17 )}{( x - 4 ) ^{2}}

\frac{d}{d x} (x^{2} + x - 17) = 2 x + 1

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

= \frac{( 2 x + 1 ) ( x - 4 ) - 1 \cdot ( x ^{2} + x - 17 )}{( x - 4 ) ^{2}}

Vereinfache

\frac{( 2 x + 1 ) ( x - 4 ) - 1 \cdot ( x ^{2} + x - 17 )}{( x - 4 ) ^{2}} : \frac{x ^{2} - 8 x + 13}{( x - 4 ) ^{2}}

= \frac{x ^{2} - 8 x + 13}{( x - 4 ) ^{2}}

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