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Beliebt Rechnen >

d/(dz)(z^5-e^zln(z))

Lösung

\frac{d}{d z} (z^{5} - e^{z} ln (z))

Lösung

5 z^{4} - e^{z} ln (z) - \frac{e ^{z}}{z}

Schritte zur Lösung

\frac{d}{d z} (z^{5} - e^{z} ln (z))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d z} (z^{5}) - \frac{d}{d z} (e^{z} ln (z))

\frac{d}{d z} (z^{5}) = 5 z^{4}

\frac{d}{d z} (e^{z} ln (z)) = e^{z} ln (z) + \frac{e ^{z}}{z}

= 5 z^{4} - (e^{z} ln (z) + \frac{e ^{z}}{z})

Vereinfache

= 5 z^{4} - e^{z} ln (z) - \frac{e ^{z}}{z}

Graph

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