derivative of (arcsec((x^2/2))^{3x})

Lösung

\frac{d}{d x} ((arcsec (\frac{x ^{2}}{2}))^{3 x})

3 arcsec^{3 x} (\frac{x ^{2}}{2}) ln (arcsec (\frac{x ^{2}}{2})) + \frac{4}{arcsec ( \frac{x ^{2}}{2} ) x ^{4} - 4}

Schritte zur Lösung

\frac{d}{d x} ((arcsec (\frac{x ^{2}}{2}))^{3 x})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

(arcsec (\frac{x ^{2}}{2}))^{3 x} = e^{3 x l n (arcsec (\frac{x ^{2}}{2}))}

= \frac{d}{d x} (e^{3 x l n (arcsec (\frac{x ^{2}}{2}))})

Wende die Kettenregel an:

e^{3 x l n (arcsec (\frac{x ^{2}}{2}))} \frac{d}{d x} (3 x ln (arcsec (\frac{x ^{2}}{2})))

= e^{3 x l n (arcsec (\frac{x ^{2}}{2}))} \frac{d}{d x} (3 x ln (arcsec (\frac{x ^{2}}{2})))

\frac{d}{d x} (3 x ln (arcsec (\frac{x ^{2}}{2}))) = 3 ln (arcsec (\frac{x ^{2}}{2})) + \frac{4 x ^{2}}{arcsec ( \frac{x ^{2}}{2} ) x ^{4} x ^{4} - 4}

= e^{3 x l n (arcsec (\frac{x ^{2}}{2}))} \cdot 3 ln (arcsec (\frac{x ^{2}}{2})) + \frac{4 x ^{2}}{arcsec ( \frac{x ^{2}}{2} ) x ^{4} x ^{4} - 4}

Vereinfache

e^{3 x l n (arcsec (\frac{x ^{2}}{2}))} \cdot 3 ln (arcsec (\frac{x ^{2}}{2})) + \frac{4 x ^{2}}{arcsec ( \frac{x ^{2}}{2} ) x ^{4} x ^{4} - 4} : 3 arcsec^{3 x} (\frac{x ^{2}}{2}) ln (arcsec (\frac{x ^{2}}{2})) + \frac{4}{arcsec ( \frac{x ^{2}}{2} ) x ^{4} - 4}

= 3 arcsec^{3 x} (\frac{x ^{2}}{2}) ln (arcsec (\frac{x ^{2}}{2})) + \frac{4}{arcsec ( \frac{x ^{2}}{2} ) x ^{4} - 4}

\int e^{s i n (x)} sin (2 x) d x

x \to 5 lim (g (x))

\int \frac{1}{48} x d x

d er i v a t i v e \frac{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}}

\int (6 x^{2}) (2 x^{3} + 1)^{2} d x