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Beliebt Rechnen >

(\partial)/(\partial x)(xcos(x)cos(y))

Lösung

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

Lösung

cos (y) (cos (x) - x sin (x))

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

= cos (y) \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)

= cos (y) (\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)

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

Vereinfache

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

Beliebte Beispiele

limit as x approaches 2 of (3x^2-5x-2)/(2x-1)

x \to 2 lim (\frac{3 x ^{2} - 5 x - 2}{2 x - 1})

y^2dx=(2xy+x^2)dy

y^{2} d x = (2 x y + x^{2}) d y

integral of 4e^{-5x}

\int 4 e^{- 5 x} d x

integral of (1-cos(x))^2

\int (1 - cos (x))^{2} d x

laplacetransform 4-4*e^{2t}

l a pl a ce t r an s f or m 4 - 4 \cdot e^{2 t}