derivative y= x/((x-2)^2)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} ((x^{2} + 1) \cdot (x + 5 + \frac{1}{x}))

\frac{d y}{d x} = e^{5 x + 4 y}

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\int 5 x cos (x) d x

in v erse l a pl a ce \frac{( s + 2 )}{( s ^{2} + 3 s + 1 )}