What is (\partial)/(\partial x)(xe^{xy}+ye^{-x}) ?

The answer to (\partial)/(\partial x)(xe^{xy}+ye^{-x}) is e^{yx}+ye^{yx}x-ye^{-x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(xe^{xy}+ye^{-x})

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

e^{y x} + y e^{y x} x - y e^{- x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= e^{y x} + y e^{y x} x - y e^{- x}

\int 1 - sin^{2} (θ) d θ

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

\int 4 y sin (x y) d x

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

\int_{0}^{1} 2 + 5 x^{2} d x

What is (\partial)/(\partial x)(xe^{xy}+ye^{-x}) ?
The answer to (\partial)/(\partial x)(xe^{xy}+ye^{-x}) is e^{yx}+ye^{yx}x-ye^{-x}