derivative f(x)=(6-x^2)/(sqrt(x))

Lösung

ableitung von

f (x) = \frac{6 - x ^{2}}{x}

\frac{- 3 x ^{2} - 6}{2 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 - x ^{2}}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 6 - x ^{2} ) x - \frac{d}{d x} ( x ) ( 6 - x ^{2} )}{( x ) ^{2}}

\frac{d}{d x} (6 - x^{2}) = - 2 x

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

= \frac{( - 2 x ) x - \frac{1}{2 x} ( 6 - x ^{2} )}{( x ) ^{2}}

Vereinfache

\frac{( - 2 x ) x - \frac{1}{2 x} ( 6 - x ^{2} )}{( x ) ^{2}} : \frac{- 3 x ^{2} - 6}{2 x x}

= \frac{- 3 x ^{2} - 6}{2 x x}

\frac{d}{d t} (2 e^{- t})

\frac{\partial}{\partial x} (y^{4} cos (5 x) \cdot 5)

\int_{0}^{\frac{5}{8}} \frac{1}{( 64 x ^{2} + 1 ) ^{\frac{3}{2}}} d x

\frac{d y}{d x} = \frac{3 e ^{x}}{y ^{2}}

l a pl a ce t r an s f or m e^{- t} \cdot (cos (4 t) - 2 sin (4 t))