(\partial)/(\partial x)(2xcos(x))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = cos (x)

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

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

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

\frac{d ^{4}}{d x ^{4}} (x^{x})

\int e^{\frac{1}{y}} d y

d er i v a t i v e 4 x - 2 x

d er i v a t i v e lo g_{2} (e^{- x} cos (π x))

im pl i c i t \frac{d y}{d x}, x^{3} - 3 x^{2} y + 2 x y^{2} = 12