derivative arcsec(x)*arccos(x)

Lösung

ableitung von

arcsec (x) \cdot arccos (x)

\frac{arccos ( x )}{x ^{2} x ^{2} - 1} - \frac{arcsec ( x )}{1 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arcsec (x) arccos (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = arcsec (x), g = arccos (x)

= \frac{d}{d x} (arcsec (x)) arccos (x) + \frac{d}{d x} (arccos (x)) arcsec (x)

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

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

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

Vereinfache

\frac{1}{x ^{2} x ^{2} - 1} arccos (x) + (- \frac{1}{1 - x ^{2}}) arcsec (x) : \frac{arccos ( x )}{x ^{2} x ^{2} - 1} - \frac{arcsec ( x )}{1 - x ^{2}}

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

\int t e^{t + 2} d t

\int \frac{d m}{m ^{3} + m ^{2}} d x

\frac{d}{d r} (\frac{1}{2 r} + \frac{1}{7 r ^{\frac{6}{7}}})

\int cos (t) sin^{4} (t) d t

\frac{d}{d x} (e^{- 5})