derivative of 2x^3cos(xsin(x))

Lösung

\frac{d}{d x} (2 x^{3} cos (x) sin (x))

3 x^{2} sin (2 x) + cos (2 x) \cdot 2 x^{3}

Schritte zur Lösung

\frac{d}{d x} (2 x^{3} cos (x) sin (x))

Vereinfache

2 x^{3} cos (x) sin (x) : x^{3} sin (2 x)

= \frac{d}{d x} (x^{3} sin (2 x))

Wende die Produktregel an:

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

f = x^{3}, g = sin (2 x)

= \frac{d}{d x} (x^{3}) sin (2 x) + \frac{d}{d x} (sin (2 x)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} sin (2 x) + cos (2 x) \cdot 2 x^{3}

n = 0 \sum \infty \frac{( - 1 ) ^{n}}{2}

t \to 0 lim (\frac{e ^{7 t} - 1}{sin ( t )})

\frac{\partial}{\partial x} (3 x + 7)

d er i v a t i v e x^{3 π}

d er i v a t i v e e^{x} + x^{e}