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Beliebt Rechnen >

d/(d{z)}(e^{3{x}+4{y}}cos(5{z}))

Lösung

\frac{d}{d z} (e^{3 x + 4 y} cos (5 z))

Lösung

- 5 e^{3 x + 4 y} sin (5 z)

Schritte zur Lösung

\frac{d}{d z} (e^{3 x + 4 y} cos (5 z))

Entferne die Konstante:

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

= e^{3 x + 4 y} \frac{d}{d z} (cos (5 z))

Wende die Kettenregel an:

- sin (5 z) \frac{d}{d z} (5 z)

= - sin (5 z) \frac{d}{d z} (5 z)

\frac{d}{d z} (5 z) = 5

= e^{3 x + 4 y} (- sin (5 z) \cdot 5)

Vereinfache

= - 5 e^{3 x + 4 y} sin (5 z)

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