(sec(x)tan(x))^'

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

(sec (x))^{'} = sec (x) tan (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 \frac{3 ( 7 x ^{2} - 2 x + 6 )}{4 x ^{\frac{5}{2}}}

\frac{\partial}{\partial x} (x y e^{z})

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

\frac{\partial}{\partial x} (x y e^{2})

\int_{1}^{3} (x + 2)^{3} d x