derivative of x/(sqrt(1-(ln(x)^2)))

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

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

\int cos (x^{2} - 5) d x

x \to 2 lim (\frac{3 ^{x}}{x + 1})

\int x e^{x + 1} d x

\int sec^{3} (v) d v

\frac{\partial}{\partial x} (x sec (y))