derivative of (-1-x/((x-1)^3))

Lösung

\frac{d}{d x} (\frac{- 1 - x}{( x - 1 ) ^{3}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{- 1 - x}{( x - 1 ) ^{3}})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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

\frac{d}{d x} (ln (e^{4}))

\frac{d}{d x} (5 x^{3} - x^{- \frac{2}{5}})

x \to 0 lim (12 + x^{2} ln (x))

\frac{d}{d x} (\frac{5 x ^{2} - 9 x + 7}{3 x + 2})