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Beliebt Rechnen >

derivative 4sec(x)tan(x)

Lösung

ableitung von

4 sec (x) tan (x)

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (4 sec (x) tan (x))

Entferne die Konstante:

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

= 4 \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)

= 4 (\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)

= 4 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x))

Vereinfache

4 (sec (x) tan (x) tan (x) + sec^{2} (x) sec (x)) : 4 (- sec (x) + 2 sec^{3} (x))

= 4 (- sec (x) + 2 sec^{3} (x))

Graph

Beliebte Beispiele

y^'=3x+y,y(0)=3

y^{^{'}} = 3 x + y, y (0) = 3

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integral of (2sin(t)cos(t))

\int (2 sin (t) cos (t)) d t

limit as n approaches infinity of n!+n^3

n \to \infty lim (n! + n^{3})

limit as x approaches 5 of 3x-7

x \to 5 lim (3 x - 7)