derivative f(x)=(1+4x)/(9-6x)

Lösung

ableitung von

f (x) = \frac{1 + 4 x}{9 - 6 x}

\frac{14}{3 ( 2 x - 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1 + 4 x}{9 - 6 x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 1 + 4 x ) ( 9 - 6 x ) - \frac{d}{d x} ( 9 - 6 x ) ( 1 + 4 x )}{( 9 - 6 x ) ^{2}}

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

\frac{d}{d x} (9 - 6 x) = - 6

= \frac{4 ( 9 - 6 x ) - ( - 6 ) ( 1 + 4 x )}{( 9 - 6 x ) ^{2}}

Vereinfache

\frac{4 ( 9 - 6 x ) - ( - 6 ) ( 1 + 4 x )}{( 9 - 6 x ) ^{2}} : \frac{14}{3 ( 2 x - 3 ) ^{2}}

= \frac{14}{3 ( 2 x - 3 ) ^{2}}

\int - x^{2} + 5 x d x

\frac{\partial}{\partial x} (\frac{3 y - 6 x}{y ^{2} + 7 x ^{2}})

\int 1 - 100 x^{2} d x

\int_{0}^{\frac{π}{2}} 10 sin^{2} (3 x) d x

x \to 1 + lim (x ln (x))