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Beliebt Rechnen >

(\partial)/(\partial x)(xcos(x+2y)*2)

Lösung

\frac{\partial}{\partial x} (x cos (x + 2 y) \cdot 2)

Lösung

2 (cos (x + 2 y) - x sin (x + 2 y))

Schritte zur Lösung

\frac{\partial}{\partial x} (x cos (x + 2 y) \cdot 2)

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = cos (x + 2 y)

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

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

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

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

Vereinfache

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

Beliebte Beispiele

derivative of x*cos(y)

\frac{d}{d x} (x \cdot cos (y))

limit as x approaches 0 of (cot(pix)sin(x))/(2sec(x))

x \to 0 lim (\frac{cot ( π x ) sin ( x )}{2 sec ( x )})

integral of cos(3t)

\int cos (3 t) d t

derivative of 2sqrt({f)(x})

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

integral of (e^{-x^2})^2

\int (e^{- x^{2}})^{2} d x