derivative y=((x-5))/(x^3)

Lösung

ableitung von

y = \frac{( x - 5 )}{x ^{3}}

\frac{- 2 x + 15}{x ^{4}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x - 5) = 1

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

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

Vereinfache

\frac{1 \cdot x ^{3} - 3 x ^{2} ( x - 5 )}{( x ^{3} ) ^{2}} : \frac{- 2 x + 15}{x ^{4}}

= \frac{- 2 x + 15}{x ^{4}}

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

s l o p e (- 3.3) (5.9)

\frac{\partial}{\partial y} (e^{2 y})

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

\int_{0}^{2} \frac{2 x}{( x ^{2} + 5 ) ^{2}} d x