derivative of 4(sin(x+xcos(x)))

Lösung

\frac{d}{d x} (4 (sin (x) + x cos (x)))

4 (2 cos (x) - x sin (x))

Schritte zur Lösung

\frac{d}{d x} (4 (sin (x) + x cos (x)))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (sin (x) + x cos (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 4 (\frac{d}{d x} (sin (x)) + \frac{d}{d x} (x cos (x)))

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

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

= 4 (cos (x) + cos (x) - x sin (x))

Vereinfache

= 4 (2 cos (x) - x sin (x))

\frac{d y}{d x} = 8 x e^{y}

\frac{d}{d x} (3^{x + 1})

\int_{4}^{5} (x^{3} - π x^{2}) d x

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

\frac{d}{d x} (4 x^{3} - 52 x^{2} + 160 x)