derivative of (xx^2cos(x))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

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

f = x^{3}, g = cos (x)

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

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

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

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

Vereinfache

= 3 x^{2} cos (x) - x^{3} sin (x)

x \to 0 lim ((1 + 2 x)^{\frac{6}{x}})

n = 2 \sum \infty ln (ln (n))

x \to 3 lim (3 x - 5)

\int + t ln (t + 5) d t

\frac{d}{d x} (\frac{3}{2 + tan ( x )})