derivative of 4^xln(x)

Lösung

\frac{d}{d x} (4^{x} ln (x))

ln (2) \cdot 2^{2 x + 1} ln (x) + \frac{4 ^{x}}{x}

Schritte zur Lösung

\frac{d}{d x} (4^{x} ln (x))

Wende die Produktregel an:

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

f = 4^{x}, g = ln (x)

= \frac{d}{d x} (4^{x}) ln (x) + \frac{d}{d x} (ln (x)) 4^{x}

\frac{d}{d x} (4^{x}) = ln (2) \cdot 2^{2 x + 1}

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

= ln (2) \cdot 2^{2 x + 1} ln (x) + \frac{1}{x} \cdot 4^{x}

\frac{1}{x} \cdot 4^{x} = \frac{4 ^{x}}{x}

= ln (2) \cdot 2^{2 x + 1} ln (x) + \frac{4 ^{x}}{x}

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