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Beliebt Rechnen >

derivative of (xcos(x)sin(x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

(\partial)/(\partial x)(e^{2(2x+y)})

\frac{\partial}{\partial x} (e^{2 (2 x + y)})

derivative ln(x^2-1)

d er i v a t i v e ln (x^{2} - 1)

sum from n=0 to infinity of nx^{n-1}

n = 0 \sum \infty n x^{n - 1}

derivative of x^{(-5/9})

\frac{d}{d x} (x^{\frac{- 5}{9}})

derivative f(x)=e^{-(x^2)/2}

d er i v a t i v e f (x) = e^{- \frac{x ^{2}}{2}}