derivative of (x+2/(x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

t a y l or tan (x), \frac{π}{4}

y^{^{'}} = \frac{2 - e ^{x}}{3 + 2 y}, y (0) = 0

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

in v erse l a pl a ce 8

d er i v a t i v e tan^{2} (x)