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Beliebt Rechnen >

(\partial)/(\partial y)(e^{xy}sin(z))

Lösung

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

Lösung

sin (z) e^{x y} x

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Beliebte Beispiele

limit as x approaches 1 of sqrt(x)

x \to 1 lim (x)

derivative of 4(x+4^{3/2})

\frac{d}{d x} (4 (x + 4)^{\frac{3}{2}})

integral of (1/x+e^x)

\int (\frac{1}{x} + e^{x}) d x

y^{''}+64y=7tan(8x)

y^{^{''}} + 64 y = 7 tan (8 x)

limit as x approaches 0 of (x^5+9x)/x

x \to 0 lim (\frac{x ^{5} + 9 x}{x})