derivative of (3x-2/(x^2))

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\int (x^{5} - 9 + \frac{6}{x ^{7}}) d x

\frac{d}{d x} (y + x) + x + y + 1 = 0

\int \frac{1}{- x ^{2} + 2 x + 8} d x

\frac{\partial}{\partial x} (2 x y + y cos (x))

a re a e^{8 x} - e^{2 x}, x = 1