derivative of x/(1-ln(x-1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

t an g e n t f (x) = 2 + 4 x^{2}, (0, 2)

t an g e n t y = \frac{8}{sin ( x ) + cos ( x )}, (0, 8)

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

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

y^{^{''}} + 34 y = 0