derivative of (1-x/(x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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

\int_{\frac{π}{2}}^{π} 4 cot (\frac{x}{2}) d x

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

\frac{d}{d x} (e^{x^{2} - 4} + 2 x + 9)

\frac{d}{d x} (tan^{4} (cot (3 x^{4} + 5 x)))