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Beliebt Rechnen >

derivative e^{7x}(7x-1)^8

Lösung

ableitung von

e^{7 x} (7 x - 1)^{8}

Lösung

e^{7 x} \cdot 7 (7 x - 1)^{8} + 56 (7 x - 1)^{7} e^{7 x}

Schritte zur Lösung

\frac{d}{d x} (e^{7 x} (7 x - 1)^{8})

Wende die Produktregel an:

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

f = e^{7 x}, g = (7 x - 1)^{8}

= \frac{d}{d x} (e^{7 x}) (7 x - 1)^{8} + \frac{d}{d x} ((7 x - 1)^{8}) e^{7 x}

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

\frac{d}{d x} ((7 x - 1)^{8}) = 56 (7 x - 1)^{7}

= e^{7 x} \cdot 7 (7 x - 1)^{8} + 56 (7 x - 1)^{7} e^{7 x}

Graph

Beliebte Beispiele

sum from n=1 to infinity of 6/(sqrt(n))

n = 1 \sum \infty \frac{6}{n}

sum from n=1 to infinity of 1/(n^{7/2)}

n = 1 \sum \infty \frac{1}{n ^{\frac{7}{2}}}

y^{^{''}} + 28 y = 0

integral of (y^2)/8

\int \frac{y ^{2}}{8} d y

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