derivative of (x(1+{z}(x))/(1-{z)(x)})

Lösung

\frac{d}{d x} (\frac{x ( 1 + z ( x ) )}{1 - z ( x )})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x ( 1 + z ( x ) )}{1 - z ( x )})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x (1 + z (x))) = 1 + z (x) + x \frac{d}{d x} (z (x))

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

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

Vereinfache

\frac{( 1 + z ( x ) + x \frac{d}{d x} ( z ( x ) ) ) ( 1 - z ( x ) ) - ( - \frac{d}{d x} ( z ( x ) ) ) x ( 1 + z ( x ) )}{( 1 - z ( x ) ) ^{2}} : \frac{2 x \frac{d}{d x} ( z ( x ) ) - z ( x ) ^{2} + 1}{( 1 - z ( x ) ) ^{2}}

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

\frac{d y}{d x} = 5 x e^{6 y}

a re a 3 x + 18, x^{2}

x \to 0 + lim (\frac{x ^{2} - 1}{x - 1})

\int \frac{1}{5 - 4 x ^{2}} d x

d er i v a t i v e sin (x) + cos (x)