What is (\partial}{\partial x}(e^{\frac{-2y)/x}) ?

The answer to (\partial}{\partial x}(e^{\frac{-2y)/x}) is (2e^{-(2y)/x}y)/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{2 e ^{- \frac{2 y}{x}} y}{x ^{2}}

Solution steps

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

Simplify

e^{\frac{- 2 y}{x}} : e^{- \frac{2 y}{x}}

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{- \frac{2 y}{x}} \frac{2 y}{x ^{2}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 e ^{- \frac{2 y}{x}} y}{x ^{2}}

\frac{d}{d x} (\frac{e ^{2 x}}{x ^{4}})

g (f) = f^{8}

\int \frac{1}{x + 5} d x

e^{- 3 t} + 3

\int \frac{- t}{( t + 1 ) - ( t + 1 )} d t

What is (\partial}{\partial x}(e^{\frac{-2y)/x}) ?
The answer to (\partial}{\partial x}(e^{\frac{-2y)/x}) is (2e^{-(2y)/x}y)/(x^2)