derivative f(x)=8sec(x)tan(x)

Lösung

ableitung von

f (x) = 8 sec (x) tan (x)

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

Schritte zur Lösung

\frac{d}{d x} (8 sec (x) tan (x))

Entferne die Konstante:

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

= 8 \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)

= 8 (\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)

= 8 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x))

Vereinfache

8 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x)) : 8 (- sec (x) + 2 sec^{3} (x))

= 8 (- sec (x) + 2 sec^{3} (x))

t an g e n t f (x) = x^{2} + 1, (0, 1)

n = 5 \sum \infty \frac{3 ^{n}}{1 2 ^{n}}

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d er i v a t i v e sin (2 π t)