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Beliebt Rechnen >

derivative of 4sec^2(4x)

Lösung

\frac{d}{d x} (4 sec^{2} (4 x))

Lösung

32 sec^{2} (4 x) tan (4 x)

Schritte zur Lösung

\frac{d}{d x} (4 sec^{2} (4 x))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (sec^{2} (4 x))

Wende die Kettenregel an:

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

= 2 sec (4 x) \frac{d}{d x} (sec (4 x))

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

= 4 \cdot 2 sec (4 x) sec (4 x) tan (4 x) \cdot 4

Vereinfache

4 \cdot 2 sec (4 x) sec (4 x) tan (4 x) \cdot 4 : 32 sec^{2} (4 x) tan (4 x)

= 32 sec^{2} (4 x) tan (4 x)

Graph

Beliebte Beispiele

derivative 5e^t

d er i v a t i v e 5 e^{t}

derivative of e^xcos(5x)

\frac{d}{d x} (e^{x} cos (5 x))

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\frac{d}{d x} (A x e^{2 x})

integral of (sqrt(4x^2-64))/x

\int \frac{4 x ^{2} - 64}{x} d x

(dy)/(dθ)=sin^4(piθ)

\frac{d y}{d θ} = sin^{4} (π θ)