derivative f(x)= x/(1-ln(x-7))

Lösung

ableitung von

f (x) = \frac{x}{1 - ln ( x - 7 )}

\frac{2 x - ln ( x - 7 ) ( x - 7 ) - 7}{( x - 7 ) ( 1 - ln ( x - 7 ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x}{1 - ln ( x - 7 )})

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 - 7 ) ) - \frac{d}{d x} ( 1 - ln ( x - 7 ) ) x}{( 1 - ln ( x - 7 ) ) ^{2}}

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

\frac{d}{d x} (1 - ln (x - 7)) = - \frac{1}{x - 7}

= \frac{1 \cdot ( 1 - ln ( x - 7 ) ) - ( - \frac{1}{x - 7} ) x}{( 1 - ln ( x - 7 ) ) ^{2}}

Vereinfache

\frac{1 \cdot ( 1 - ln ( x - 7 ) ) - ( - \frac{1}{x - 7} ) x}{( 1 - ln ( x - 7 ) ) ^{2}} : \frac{2 x - ln ( x - 7 ) ( x - 7 ) - 7}{( x - 7 ) ( 1 - ln ( x - 7 ) ) ^{2}}

= \frac{2 x - ln ( x - 7 ) ( x - 7 ) - 7}{( x - 7 ) ( 1 - ln ( x - 7 ) ) ^{2}}

y^{^{'}} = \frac{( ln ^{2} ( x ) )}{3 x}

d er i v a t i v e y = x^{2} - 3 x

x \to - 3 - lim (h (x))

s l o p e in t erce pt (1.7) (6.1)

\frac{d}{d x} (arctan (x + 1))