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Beliebt Rechnen >

(\partial)/(\partial x)(ysin(xy))

Lösung

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

Lösung

y^{2} cos (y x)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= y cos (x y) y

Vereinfache

y cos (x y) y : y^{2} cos (y x)

= y^{2} cos (y x)

Beliebte Beispiele

(dy)/(dx)=(9x^2-6)/(x^2)

\frac{d y}{d x} = \frac{9 x ^{2} - 6}{x ^{2}}

(\partial)/(\partial y)(xe^y-x^5+y-3)

\frac{\partial}{\partial y} (x e^{y} - x^{5} + y - 3)

derivative of x/(x^2+y^2+1)

\frac{d}{d x} (\frac{x}{x ^{2} + y ^{2} + 1})

(d^2)/(dx^2)(e^{-3x})

\frac{d ^{2}}{d x ^{2}} (e^{- 3 x})

integral from 0 to 1 of-8x5^x

\int_{0}^{1} - 8 x 5^{x} d x