derivative of ((x+1^5)/((1-x)^4))

Lösung

\frac{d}{d x} (\frac{( x + 1 ) ^{5}}{( 1 - x ) ^{4}})

\frac{( x + 1 ) ^{4} ( - x + 9 )}{( 1 - x ) ^{5}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( x + 1 ) ^{5}}{( 1 - x ) ^{4}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ( x + 1 ) ^{5} ) ( 1 - x ) ^{4} - \frac{d}{d x} ( ( 1 - x ) ^{4} ) ( x + 1 ) ^{5}}{( ( 1 - x ) ^{4} ) ^{2}}

\frac{d}{d x} ((x + 1)^{5}) = 5 (x + 1)^{4}

\frac{d}{d x} ((1 - x)^{4}) = - 4 (1 - x)^{3}

= \frac{5 ( x + 1 ) ^{4} ( 1 - x ) ^{4} - ( - 4 ( 1 - x ) ^{3} ) ( x + 1 ) ^{5}}{( ( 1 - x ) ^{4} ) ^{2}}

Vereinfache

\frac{5 ( x + 1 ) ^{4} ( 1 - x ) ^{4} - ( - 4 ( 1 - x ) ^{3} ) ( x + 1 ) ^{5}}{( ( 1 - x ) ^{4} ) ^{2}} : \frac{( x + 1 ) ^{4} ( - x + 9 )}{( 1 - x ) ^{5}}

= \frac{( x + 1 ) ^{4} ( - x + 9 )}{( 1 - x ) ^{5}}

d er i v a t i v e y = ln (e^{3 x})

x \to 49 lim (\frac{x ^{2}}{7} - \frac{7}{x})

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

t a y l or 3 x, 27

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