derivative of sec(x*tan(x))

Lösung

\frac{d}{d x} (sec (x) \cdot tan (x))

- sec (x) + 2 sec^{3} (x)

Schritte zur Lösung

\frac{d}{d x} (sec (x) tan (x))

Wende die Produktregel an:

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

f = sec (x), g = tan (x)

= \frac{d}{d x} (sec (x)) tan (x) + \frac{d}{d x} (tan (x)) sec (x)

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

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

= sec (x) tan (x) tan (x) + sec^{2} (x) sec (x)

Vereinfache

sec (x) tan (x) tan (x) + sec^{2} (x) sec (x) : - sec (x) + 2 sec^{3} (x)

= - sec (x) + 2 sec^{3} (x)

d er i v a t i v e tan (3 x^{2})

x \to 0 lim (e^{- c o t (x)})

d er i v a t i v e f (2) = 3 - x^{2}

d er i v a t i v e f (x) = \frac{2}{x ^{2}}

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