(\partial)/(\partial x)(2xsin(xy))

Lösung

\frac{\partial}{\partial x} (2 x sin (x y))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x sin (x y))

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = sin (x y)

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

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

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

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

Vereinfache

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

x v^{'} + 2 v = 0

x y^{^{'}} = 2 y + x^{3} cos (x)

\int cos^{5} (x) sin^{4} (x) d x

\frac{d y}{d x} 0.4 x y = 9 x

\int_{2}^{10} \frac{x ^{2} + 36}{12 x} d x