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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

x \to \infty lim (g (x))

t an g e n t f (x) = e^{x^{7}}, (- 1, \frac{1}{e})

d er i v a t i v e y = x^{3} - 3 x

\frac{d}{d x} (\frac{1 + sin ( x )}{1 + cos ( x )})

d er i v a t i v e (2 r a^{r x} + n)^{p}