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Beliebt Rechnen >

(\partial)/(\partial x)(2e^{5xy})

Lösung

\frac{\partial}{\partial x} (2 e^{5 x y})

Lösung

10 e^{5 x y} y

Schritte zur Lösung

\frac{\partial}{\partial x} (2 e^{5 x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 2 \frac{\partial}{\partial x} (e^{5 x y})

Wende die Kettenregel an:

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

= e^{5 x y} \frac{\partial}{\partial x} (5 x y)

\frac{\partial}{\partial x} (5 x y) = 5 y

= 2 e^{5 x y} \cdot 5 y

Vereinfache

= 10 e^{5 x y} y

Beliebte Beispiele

(\partial)/(\partial x)((y^2)/(1+x^2))

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

(\frac{3 x ^{2}}{2})^{^{'}}

d/(dy)((4x-2y)/(4x+2y))

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

derivative of sqrt({r)(x(x)^2-x^2})

\frac{d}{d x} (r (x) (x)^{2} - x^{2})

derivative of (1+e^x^3)

\frac{d}{d x} ((1 + e^{x})^{3})