derivative of ln(sqrt((1-sin(x)/(1+sin(x)))))

Lösung

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

- sec (x)

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{\frac{1 - s i n ( x )}{1 + s i n ( x )}} \frac{d}{d x} (\frac{1 - sin ( x )}{1 + sin ( x )})

= \frac{1}{\frac{1 - s i n ( x )}{1 + s i n ( x )}} \frac{d}{d x} (\frac{1 - sin ( x )}{1 + sin ( x )})

\frac{d}{d x} (\frac{1 - sin ( x )}{1 + sin ( x )}) = - \frac{cos ( x )}{- sin ( x ) + 1 ( sin ( x ) + 1 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{1 - s i n ( x )}{1 + s i n ( x )}} (- \frac{cos ( x )}{- sin ( x ) + 1 ( sin ( x ) + 1 ) ^{\frac{3}{2}}})

Vereinfache

\frac{1}{\frac{1 - s i n ( x )}{1 + s i n ( x )}} (- \frac{cos ( x )}{- sin ( x ) + 1 ( sin ( x ) + 1 ) ^{\frac{3}{2}}}) : - sec (x)

= - sec (x)

\int \frac{( y - 2 ) ^{2}}{y} d y

t an g e n t 100 x^{2} + 400 x + 5000

\int \frac{x}{x ^{4} + 6 x ^{2} + 10} d x

\int tan (θ) sec (θ) sec^{2} (θ) d θ

\frac{d}{d x} (ln (4 + ln (x)))