(1/4 x^8-3e^x+100ln(x))^'

Lösung

(\frac{1}{4} x^{8} - 3 e^{x} + 100 ln (x))^{^{'}}

2 x^{7} - 3 e^{x} + \frac{100}{x}

Schritte zur Lösung

(\frac{1}{4} x^{8} - 3 e^{x} + 100 ln (x))^{'}

Vereinfache

\frac{1}{4} x^{8} - 3 e^{x} + 100 ln (x) : \frac{x ^{8}}{4} - 3 e^{x} + 100 ln (x)

= (\frac{x ^{8}}{4} - 3 e^{x} + 100 ln (x))^{^{'}}

Wende die Summen-/Differenzregel an:

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

= (\frac{x ^{8}}{4})^{^{'}} - (3 e^{x})^{^{'}} + (100 ln (x))^{^{'}}

(\frac{x ^{8}}{4})^{'} = 2 x^{7}

(3 e^{x})^{'} = 3 e^{x}

(100 ln (x))^{'} = \frac{100}{x}

= 2 x^{7} - 3 e^{x} + \frac{100}{x}

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