derivative y=sec(x)tan(x)

Lösung

ableitung von

y = sec (x) 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)

\int 7 e^{3 x} d x

\frac{\partial}{\partial y} (\frac{2}{2 x + 3 y})

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

\frac{d}{d x} (- x^{3} + 9 x^{2} - 6 x + 9)

d er i v a t i v e \frac{8}{64 + 64 t ^{2}}