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Beliebt Rechnen >

derivative of 8^xln(x)

Lösung

\frac{d}{d x} (8^{x} ln (x))

Lösung

3 ln (2) \cdot 8^{x} ln (x) + \frac{8 ^{x}}{x}

Schritte zur Lösung

\frac{d}{d x} (8^{x} ln (x))

Wende die Produktregel an:

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

f = 8^{x}, g = ln (x)

= \frac{d}{d x} (8^{x}) ln (x) + \frac{d}{d x} (ln (x)) 8^{x}

\frac{d}{d x} (8^{x}) = 3 ln (2) \cdot 8^{x}

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 3 ln (2) \cdot 8^{x} ln (x) + \frac{1}{x} \cdot 8^{x}

\frac{1}{x} \cdot 8^{x} = \frac{8 ^{x}}{x}

= 3 ln (2) \cdot 8^{x} ln (x) + \frac{8 ^{x}}{x}

Graph

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