derivative 2xcos(x)

Lösung

ableitung von

2 x cos (x)

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = cos (x)

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

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

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

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

Vereinfache

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

\int \frac{1}{4 + ( x - 3 ) ^{2}} d x

\int (sin (π x)) d x

\frac{\partial}{\partial y} (5 z e^{x yz})

\frac{\partial}{\partial x} (e^{x y} tan (y))

h \to 0 lim (\frac{( 18 h + 1 - 1 )}{h})