derivative y=((x^2+1))/(x^3)

Lösung

ableitung von

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

\frac{- x ^{2} - 3}{x ^{4}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{- x ^{2} - 3}{x ^{4}}

d er i v a t i v e t^{2} + 1

d er i v a t i v e x^{3} - 3^{x}

d er i v a t i v e f (x) = - x + 2

d er i v a t i v e y = \frac{x ^{2} - x + 1}{a ^{3} - 3}

d er i v a t i v e y = t^{2}