derivative of 5xsin(xcos(x))

Lösung

\frac{d}{d x} (5 x sin (x) cos (x))

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

Schritte zur Lösung

\frac{d}{d x} (5 x sin (x) cos (x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (x sin (x) cos (x))

Wende die Produktregel an:

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

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

= 5 (\frac{d x}{d x} sin (x) cos (x) + \frac{d}{d x} (sin (x) cos (x)) x)

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

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

= 5 (1 \cdot sin (x) cos (x) + cos (2 x) x)

Vereinfache

= 5 (sin (x) cos (x) + x cos (2 x))

\int (3 - x) d x

\int_{0}^{l n (π)} 2 x e^{x^{2}} cos (e^{x^{2}}) d x

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

\frac{\partial}{\partial x} (1 + 2 x)

a re a 9 - x^{2}, x