derivative f(x)=((8x+7)/(9x^2+6))

Lösung

ableitung von

f (x) = (\frac{8 x + 7}{9 x ^{2} + 6})

- \frac{2 ( 12 x ^{2} + 21 x - 8 )}{3 ( 3 x ^{2} + 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x + 7}{9 x ^{2} + 6})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 8 x + 7 ) ( 9 x ^{2} + 6 ) - \frac{d}{d x} ( 9 x ^{2} + 6 ) ( 8 x + 7 )}{( 9 x ^{2} + 6 ) ^{2}}

\frac{d}{d x} (8 x + 7) = 8

\frac{d}{d x} (9 x^{2} + 6) = 18 x

= \frac{8 ( 9 x ^{2} + 6 ) - 18 x ( 8 x + 7 )}{( 9 x ^{2} + 6 ) ^{2}}

Vereinfache

\frac{8 ( 9 x ^{2} + 6 ) - 18 x ( 8 x + 7 )}{( 9 x ^{2} + 6 ) ^{2}} : - \frac{2 ( 12 x ^{2} + 21 x - 8 )}{3 ( 3 x ^{2} + 2 ) ^{2}}

= - \frac{2 ( 12 x ^{2} + 21 x - 8 )}{3 ( 3 x ^{2} + 2 ) ^{2}}

a re a y = cos (x), y = sin (x)

a re a 7 e^{x}, 7 x e^{x^{2}}, [0, 1]

\int (\frac{1}{2} x + 3)^{2} d x

n = 1 \sum \infty \frac{5}{2 ^{n - 1}}

\frac{\partial}{\partial x} (\frac{x - z}{y + z})