derivative of 6x^5e^{6x}

Lösung

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

6 (5 x^{4} e^{6 x} + e^{6 x} \cdot 6 x^{5})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{5}, g = e^{6 x}

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

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

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

= 6 (5 x^{4} e^{6 x} + e^{6 x} \cdot 6 x^{5})

\frac{d}{d x} (\frac{1 - 2 x}{6 + x})

t an g e n t f (x) = 4 x - 3 x

\frac{d}{d x} (a x^{n})

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