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Beliebt Rechnen >

(\partial)/(\partial y)(9ze^{xyz})

Lösung

\frac{\partial}{\partial y} (9 z e^{x yz})

Lösung

9 e^{z x y} z^{2} x

Schritte zur Lösung

\frac{\partial}{\partial y} (9 z e^{x yz})

Behandle

z, x

als Konstanten

Entferne die Konstante:

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

= 9 z \frac{\partial}{\partial y} (e^{x yz})

Wende die Kettenregel an:

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

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

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

= 9 z e^{x yz} z x

Vereinfache

9 z e^{x yz} z x : 9 e^{z x y} z^{2} x

= 9 e^{z x y} z^{2} x

Beliebte Beispiele

integral from 0 to pi of 2sin(nx)

\int_{0}^{π} 2 sin (n x) d x

derivative f(x)=sqrt(14x)

d er i v a t i v e f (x) = 14 x

derivative of 2arctan(e^x)

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

derivative of 8(x+2^{3/2})

\frac{d}{d x} (8 (x + 2)^{\frac{3}{2}})

derivative of-2x^4+3x^3-x^2

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