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Beliebt Rechnen >

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

Lösung

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

Lösung

2 y (e^{x y^{2}} x y^{2} + e^{x y^{2}})

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = e^{x y^{2}}, g = x

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

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

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

= 2 y (e^{x y^{2}} y^{2} x + 1 \cdot e^{x y^{2}})

Vereinfache

= 2 y (e^{x y^{2}} x y^{2} + e^{x y^{2}})

Beliebte Beispiele

(\partial)/(\partial x)(ce^{-2x}+e^{-x})

\frac{\partial}{\partial x} (c e^{- 2 x} + e^{- x})

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

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

derivative f(x)=(x^2)/(1+2x)

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

limit as x approaches 0 of 1-(x^2)/6

x \to 0 lim (1 - \frac{x ^{2}}{6})

derivative of sqrt(x)-2e^x

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