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Beliebt Rechnen >

(\partial)/(\partial y)(e^ysin(x)y)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = e^{y}, g = y

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

\frac{\partial}{\partial y} (e^{y}) = e^{y}

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

= sin (x) (e^{y} y + 1 \cdot e^{y})

Vereinfache

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

Beliebte Beispiele

integral of (x^2sin(x)-2x+3)/(x^2)

\int \frac{x ^{2} sin ( x ) - 2 x + 3}{x ^{2}} d x

(dy)/(dt)=-6/((2000+6t))

\frac{d y}{d t} = - \frac{6}{( 2000 + 6 t )}

integral of (e^x)/(e^{2x)-1}

\int \frac{e ^{x}}{e ^{2 x} - 1} d x

derivative (1/2)^x-x

d er i v a t i v e (\frac{1}{2})^{x} - x

integral from-1 to 1 of 3/4 x^2(1-x^2)

\int_{- 1}^{1} \frac{3}{4} x^{2} (1 - x^{2}) d x