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Beliebt Rechnen >

derivative of x^8(x-1^7)

Lösung

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

Lösung

8 x^{7} (x - 1)^{7} + 7 (x - 1)^{6} x^{8}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} ((x - 1)^{7}) = 7 (x - 1)^{6}

= 8 x^{7} (x - 1)^{7} + 7 (x - 1)^{6} x^{8}

Graph

Beliebte Beispiele

integral of (2x-4)

\int (2 x - 4) d x

integral of (-3/7 x^5+1/5 x^3-7/4 x^2)

\int (- \frac{3}{7} x^{5} + \frac{1}{5} x^{3} - \frac{7}{4} x^{2}) d x

derivative of 6x+3

\frac{d}{d x} (6 x + 3)

limit as x approaches 3 of (x^2+1)/(x+3)

x \to 3 lim (\frac{x ^{2} + 1}{x + 3})

y^'=sqrt(y),y(1)=1

y^{^{'}} = y, y (1) = 1