(\partial)/(\partial x)(x/((1-x)^2))

Lösung

\frac{\partial}{\partial x} (\frac{x}{( 1 - x ) ^{2}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x}{( 1 - x ) ^{2}})

Wende die Quotientenregel an:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

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

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

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

t an g e n t f (x) = x^{2} + 3, at x = 1

x \to - 10 - lim (\frac{x + 9}{x + 10})

\frac{\partial}{\partial x} (2 e^{- y} x)

\int \frac{sin ( 2 x )}{37 + cos ^{2} ( x )} d x