derivative of arcsec(x^{10})

Lösung

\frac{d}{d x} (arcsec (x^{10}))

\frac{10}{x x ^{20} - 1}

Schritte zur Lösung

\frac{d}{d x} (arcsec (x^{10}))

Wende die Kettenregel an:

\frac{1}{( x ^{10} ) ^{2} ( x ^{10} ) ^{2} - 1} \frac{d}{d x} (x^{10})

= \frac{1}{( x ^{10} ) ^{2} ( x ^{10} ) ^{2} - 1} \frac{d}{d x} (x^{10})

\frac{d}{d x} (x^{10}) = 10 x^{9}

= \frac{1}{( x ^{10} ) ^{2} ( x ^{10} ) ^{2} - 1} \cdot 10 x^{9}

Vereinfache

\frac{1}{( x ^{10} ) ^{2} ( x ^{10} ) ^{2} - 1} \cdot 10 x^{9} : \frac{10}{x x ^{20} - 1}

= \frac{10}{x x ^{20} - 1}

\frac{d}{d x} ((cos (π x - 16))^{4})

\int \frac{1}{- x ^{2} - 6 x} d x

a re a x = - y, x = 2 y + 3, y = - 2, y = 1

\frac{d}{d x} (x ln (3))

d er i v a t i v e f (x) = x + 1