derivative of arcsec(5x^4)

Lösung

\frac{d}{d x} (arcsec (5 x^{4}))

\frac{4}{x 25 x ^{8} - 1}

Schritte zur Lösung

\frac{d}{d x} (arcsec (5 x^{4}))

Wende die Kettenregel an:

\frac{1}{( 5 x ^{4} ) ^{2} ( 5 x ^{4} ) ^{2} - 1} \frac{d}{d x} (5 x^{4})

= \frac{1}{( 5 x ^{4} ) ^{2} ( 5 x ^{4} ) ^{2} - 1} \frac{d}{d x} (5 x^{4})

\frac{d}{d x} (5 x^{4}) = 20 x^{3}

= \frac{1}{( 5 x ^{4} ) ^{2} ( 5 x ^{4} ) ^{2} - 1} \cdot 20 x^{3}

Vereinfache

\frac{1}{( 5 x ^{4} ) ^{2} ( 5 x ^{4} ) ^{2} - 1} \cdot 20 x^{3} : \frac{4}{x 25 x ^{8} - 1}

= \frac{4}{x 25 x ^{8} - 1}

d er i v a t i v e cos (3 y)

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