derivative of 2^{3x+1}ln(5x-11)

Lösung

\frac{d}{d x} (2^{3 x + 1} ln (5 x - 11))

3 ln (2) \cdot 2^{3 x + 1} ln (5 x - 11) + \frac{5 \cdot 2 ^{3 x + 1}}{5 x - 11}

Schritte zur Lösung

\frac{d}{d x} (2^{3 x + 1} ln (5 x - 11))

Wende die Produktregel an:

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

f = 2^{3 x + 1}, g = ln (5 x - 11)

= \frac{d}{d x} (2^{3 x + 1}) ln (5 x - 11) + \frac{d}{d x} (ln (5 x - 11)) 2^{3 x + 1}

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

\frac{d}{d x} (ln (5 x - 11)) = \frac{5}{5 x - 11}

= 3 ln (2) \cdot 2^{3 x + 1} ln (5 x - 11) + \frac{5}{5 x - 11} \cdot 2^{3 x + 1}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 3 ln (2) \cdot 2^{3 x + 1} ln (5 x - 11) + \frac{5 \cdot 2 ^{3 x + 1}}{5 x - 11}

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