What is (\partial)/(\partial x)(-xe^{x/y}) ?

The answer to (\partial)/(\partial x)(-xe^{x/y}) is -e^{x/y}-(e^{x/y}x)/y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(-xe^{x/y})

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

- e^{\frac{x}{y}} - \frac{e ^{\frac{x}{y}} x}{y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{\frac{x}{y}}

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

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

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

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

Simplify

- (1 \cdot e^{\frac{x}{y}} + \frac{e ^{\frac{x}{y}}}{y} x) : - e^{\frac{x}{y}} - \frac{e ^{\frac{x}{y}} x}{y}

= - e^{\frac{x}{y}} - \frac{e ^{\frac{x}{y}} x}{y}

x \to 2 lim (13 - 2 x)

x \to 0 lim (8 x + 4 h - 3)

\frac{d}{d x} (1 - \frac{x ^{2}}{4})

\frac{\partial}{\partial v} (v sin (u))

\int_{0}^{1} \frac{6}{x ( x + 1 )} d x

What is (\partial)/(\partial x)(-xe^{x/y}) ?
The answer to (\partial)/(\partial x)(-xe^{x/y}) is -e^{x/y}-(e^{x/y}x)/y