derivative f(x)=(3x+5)/(1-x^2)

Lösung

ableitung von

f (x) = \frac{3 x + 5}{1 - x ^{2}}

\frac{3 + 3 x ^{2} + 10 x}{( 1 - x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x + 5}{1 - x ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 3 x + 5 ) ( 1 - x ^{2} ) - \frac{d}{d x} ( 1 - x ^{2} ) ( 3 x + 5 )}{( 1 - x ^{2} ) ^{2}}

\frac{d}{d x} (3 x + 5) = 3

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

= \frac{3 ( 1 - x ^{2} ) - ( - 2 x ) ( 3 x + 5 )}{( 1 - x ^{2} ) ^{2}}

Vereinfache

\frac{3 ( 1 - x ^{2} ) - ( - 2 x ) ( 3 x + 5 )}{( 1 - x ^{2} ) ^{2}} : \frac{3 + 3 x ^{2} + 10 x}{( 1 - x ^{2} ) ^{2}}

= \frac{3 + 3 x ^{2} + 10 x}{( 1 - x ^{2} ) ^{2}}

t an g e n t f (x) = \frac{10 x}{x ^{2} - 6}

\int \frac{x ^{5}}{e ^{2 - 3 x^{6}}} d x

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

d er i v a t i v e 3 t

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