derivative of (1-x^2/x)

Lösung

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

\frac{- x ^{2} - 1}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d x}{d x} = 1

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

Vereinfache

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

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

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

d er i v a t i v e y = \frac{8}{x - 7}

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

\int x^{27} e^{- x^{28}} d x

\int_{- 2}^{5} ∣ x - 2 ∣ d x