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Beliebt Rechnen >

derivative of xln(xcos(x))

Lösung

\frac{d}{d x} (x ln (x) cos (x))

Lösung

ln (x) cos (x) + cos (x) - x sin (x) ln (x)

Schritte zur Lösung

\frac{d}{d x} (x ln (x) cos (x))

Wende die Produktregel an:

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

f = x, g = ln (x) cos (x)

= \frac{d x}{d x} ln (x) cos (x) + \frac{d}{d x} (ln (x) cos (x)) x

\frac{d x}{d x} = 1

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

= 1 \cdot ln (x) cos (x) + (\frac{cos ( x )}{x} - sin (x) ln (x)) x

Vereinfache

1 \cdot ln (x) cos (x) + (\frac{cos ( x )}{x} - sin (x) ln (x)) x : ln (x) cos (x) + cos (x) - x sin (x) ln (x)

= ln (x) cos (x) + cos (x) - x sin (x) ln (x)

Graph

Beliebte Beispiele

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

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

d/(dθ)(cot^2(sin(θ)))

\frac{d}{d θ} (cot^{2} (sin (θ)))

d/(dt)(e^{4t}cos(t))

\frac{d}{d t} (e^{4 t} cos (t))

derivative of (7x-4/(-3x+3))

\frac{d}{d x} (\frac{7 x - 4}{- 3 x + 3})

d er i v a t i v e - 6