derivative f(x)=(x+9)/(x^2-7x+1)

Lösung

ableitung von

f (x) = \frac{x + 9}{x ^{2} - 7 x + 1}

\frac{- x ^{2} - 18 x + 64}{( x ^{2} - 7 x + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 9}{x ^{2} - 7 x + 1})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x + 9 ) ( x ^{2} - 7 x + 1 ) - \frac{d}{d x} ( x ^{2} - 7 x + 1 ) ( x + 9 )}{( x ^{2} - 7 x + 1 ) ^{2}}

\frac{d}{d x} (x + 9) = 1

\frac{d}{d x} (x^{2} - 7 x + 1) = 2 x - 7

= \frac{1 \cdot ( x ^{2} - 7 x + 1 ) - ( 2 x - 7 ) ( x + 9 )}{( x ^{2} - 7 x + 1 ) ^{2}}

Vereinfache

\frac{1 \cdot ( x ^{2} - 7 x + 1 ) - ( 2 x - 7 ) ( x + 9 )}{( x ^{2} - 7 x + 1 ) ^{2}} : \frac{- x ^{2} - 18 x + 64}{( x ^{2} - 7 x + 1 ) ^{2}}

= \frac{- x ^{2} - 18 x + 64}{( x ^{2} - 7 x + 1 ) ^{2}}

\int x \cdot sin (x^{2}) d x

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s im pl i f y ln ((5 x + 2) (3 x - 4)^{2})

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