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Beliebt Rechnen >

derivative of xsin(xcos(x))

Lösung

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

Lösung

sin (x) cos (x) + x cos (2 x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (sin (x) cos (x)) = cos (2 x)

= 1 \cdot sin (x) cos (x) + cos (2 x) x

Vereinfache

= sin (x) cos (x) + x cos (2 x)

Graph

Beliebte Beispiele

integral of x^{10}

\int x^{10} d x

integral from 0 to 2 of e^{-3x}

\int_{0}^{2} e^{- 3 x} d x

y^{''}+y^'-6y=6t-7-(20te^{2t}+14e^{2t})

y^{^{''}} + y^{^{'}} - 6 y = 6 t - 7 - (20 t e^{2 t} + 14 e^{2 t})

tangent f(x)=x^6,\at x=2

t an g e n t f (x) = x^{6}, at x = 2

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