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Beliebt Rechnen >

(\partial)/(\partial x)(e^{-x}sin(x+y))

Lösung

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

Lösung

- e^{- x} sin (x + y) + e^{- x} cos (x + y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = e^{- x}, g = sin (x + y)

= \frac{\partial}{\partial x} (e^{- x}) sin (x + y) + \frac{\partial}{\partial x} (sin (x + y)) e^{- x}

\frac{\partial}{\partial x} (e^{- x}) = - e^{- x}

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

= (- e^{- x}) sin (x + y) + cos (x + y) e^{- x}

Vereinfache

= - e^{- x} sin (x + y) + e^{- x} cos (x + y)

Beliebte Beispiele

derivative of 0.5x^2

\frac{d}{d x} (0.5 x^{2})

(\partial)/(\partial y)(y/(x^2))

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

inverselaplace 2/((s^2+4))

in v erse l a pl a ce \frac{2}{( s ^{2} + 4 )}

fläche y=x,y=2xsqrt(1-x^2)

a re a y = x, y = 2 x 1 - x^{2}

derivative of e^xsin(x^2)

\frac{d}{d x} (e^{x} sin (x^{2}))