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Beliebt Rechnen >

derivative f(x)=x^7cos(x)

Lösung

ableitung von

f (x) = x^{7} cos (x)

Lösung

7 x^{6} cos (x) - x^{7} sin (x)

Schritte zur Lösung

\frac{d}{d x} (x^{7} cos (x))

Wende die Produktregel an:

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

f = x^{7}, g = cos (x)

= \frac{d}{d x} (x^{7}) cos (x) + \frac{d}{d x} (cos (x)) x^{7}

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

\frac{d}{d x} (cos (x)) = - sin (x)

= 7 x^{6} cos (x) + (- sin (x)) x^{7}

Vereinfache

= 7 x^{6} cos (x) - x^{7} sin (x)

Graph

Beliebte Beispiele

integral of (2x+5)^3

\int (2 x + 5)^{3} d x

integral from 0 to 1 of 3/(x^5)

\int_{0}^{1} \frac{3}{x ^{5}} d x

integral of (e^x+sin(x)+x)

\int (e^{x} + sin (x) + x) d x

integral of 6x-x^2

\int 6 x - x^{2} d x

derivative of 3x^2-2x-8

\frac{d}{d x} (3 x^{2} - 2 x - 8)