derivative of 1/20 e^x+x^6-x^e+e

Lösung

\frac{d}{d x} (\frac{1}{20} e^{x} + x^{6} - x^{e} + e)

6 x^{5} - e x^{e - 1} + \frac{1}{20} e^{x}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{20} e^{x} + x^{6} - x^{e} + e)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{1}{20} e^{x}) + \frac{d}{d x} (x^{6}) - \frac{d}{d x} (x^{e}) + \frac{d e}{d x}

\frac{d}{d x} (\frac{1}{20} e^{x}) = \frac{1}{20} e^{x}

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (x^{e}) = e x^{e - 1}

\frac{d e}{d x} = 0

= \frac{1}{20} e^{x} + 6 x^{5} - e x^{e - 1} + 0

Vereinfache

= 6 x^{5} - e x^{e - 1} + \frac{1}{20} e^{x}

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