derivative of (4x-1/(x^2))

Lösung

\frac{d}{d x} (\frac{4 x - 1}{x ^{2}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{4 x - 1}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 4 x - 1 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 4 x - 1 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (4 x - 1) = 4

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

= \frac{4 x ^{2} - 2 x ( 4 x - 1 )}{( x ^{2} ) ^{2}}

Vereinfache

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

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

\frac{\partial}{\partial x} (- 6 y^{2} + 12 x y)

\frac{\partial}{\partial x} (\frac{( p ( q , x ) - c q )}{x})

\frac{\partial}{\partial y} (8 z e^{x yz})

l a pl a ce t r an s f or m f (t) = 4 t - 10

\frac{d}{d x} (\frac{x ^{5}}{7})