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Beliebt Rechnen >

(\partial)/(\partial x)(xysin(xy))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

= y \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)

= y (\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

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

Vereinfache

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

Beliebte Beispiele

integral of (e^x)/(4+e^x)

\int \frac{e ^{x}}{4 + e ^{x}} d x

d/(dt)(sqrt(t^2+1))

\frac{d}{d t} (t^{2} + 1)

(dy)/(dt)=(t^2)/(y(1+t^3))

\frac{d y}{d t} = \frac{t ^{2}}{y ( 1 + t ^{3} )}

integral from 3 to 4 of x/8

\int_{3}^{4} \frac{x}{8} d x

(\partial)/(\partial r)(pir^2h)

\frac{\partial}{\partial r} (π r^{2} h)