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

Lösung

ableitung von

h (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}}

\frac{d}{d x} (3 x^{2})

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

\frac{d}{d x} (\frac{1}{12} (x + 2)^{3} + (x + 2)^{- 1})

x \to 0 lim (\frac{7 ^{x} - 9 ^{x}}{x})

d er i v a t i v e g (t) = 4 t^{- \frac{1}{8}}