derivative 2sec^2(x)tan(x)

Lösung

ableitung von

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

- 4 sec^{2} (x) + 6 sec^{4} (x)

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

f = sec^{2} (x), g = tan (x)

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

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

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

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

Vereinfache

2 (2 sec^{2} (x) tan (x) tan (x) + sec^{2} (x) sec^{2} (x)) : - 4 sec^{2} (x) + 6 sec^{4} (x)

= - 4 sec^{2} (x) + 6 sec^{4} (x)

d er i v a t i v e cot (x^{2} + π x)

in v erse l a pl a ce \frac{s + 1}{( s ^{2} + 2 ) ( s + 1 )}

d er i v a t i v e 9 sin (2 x)

t an g e n t f (x) = \frac{x}{4 + x ^{2}}

(4^{x})^{^{'}}