derivative of sec^5(sqrt(x^2-1))

Lösung

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

\frac{5 x sec ^{5} ( x ^{2} - 1 ) tan ( x ^{2} - 1 )}{x ^{2} - 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

5 sec^{4} (x^{2} - 1) \frac{x sec ( x ^{2} - 1 ) tan ( x ^{2} - 1 )}{x ^{2} - 1} : \frac{5 x sec ^{5} ( x ^{2} - 1 ) tan ( x ^{2} - 1 )}{x ^{2} - 1}

= \frac{5 x sec ^{5} ( x ^{2} - 1 ) tan ( x ^{2} - 1 )}{x ^{2} - 1}

d er i v a t i v e 3 x^{2} + 1

f (x) = x^{\frac{1}{9}}

t an g e n t f (x) = 2 x (2 - 4 x)^{4}, at x = 1

\frac{d}{d x} (x - 2 2)

\int \frac{tan ^{2} ( x )}{sec ^{3} ( x )} d x