(\partial)/(\partial x)(3xcos(xy))

Lösung

\frac{\partial}{\partial x} (3 x cos (x y))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x cos (x y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial x} (x cos (x y))

Wende die Produktregel an:

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

f = x, g = cos (x y)

= 3 (\frac{\partial}{\partial x} (x) cos (x y) + \frac{\partial}{\partial x} (cos (x y)) x)

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

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

= 3 (1 \cdot cos (x y) + (- sin (x y) y) x)

Vereinfache

= 3 (cos (x y) - x y sin (x y))

\int (\frac{d y}{1}) d x

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\int_{0}^{\frac{π}{2}} cos^{6} (x) d x

\frac{d}{d x} (- sin (5 x) \cdot 5)

\int sec^{2} (x) tan (x) e^{s e c (x)} d x