What is the derivative of e^{(-x/y}) ?

The derivative of e^{(-x/y}) is -(e^{-x/y}(y-x\frac{dy)/(dx))}{y^2}

What is the first derivative of e^{(-x/y}) ?

The first derivative of e^{(-x/y}) is -(e^{-x/y}(y-x\frac{dy)/(dx))}{y^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Simplify

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (- \frac{x}{y}) = - \frac{y - x \frac{d y}{d x}}{y ^{2}}

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

Simplify

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

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

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

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

\int \frac{81 - x ^{2}}{x ^{2}} d x

y = 3 x^{4} - 12 x^{3}

x \to - 1 lim (x)

What is the derivative of e^{(-x/y}) ?
The derivative of e^{(-x/y}) is -(e^{-x/y}(y-x\frac{dy)/(dx))}{y^2}
What is the first derivative of e^{(-x/y}) ?
The first derivative of e^{(-x/y}) is -(e^{-x/y}(y-x\frac{dy)/(dx))}{y^2}