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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

(10.2) (19.14)

x \to 2 + lim (\frac{∣ 2 - x ∣}{2 - x})

\int \frac{8}{9 + 8 x} d x

y = 2 ln (2 x)

\int \frac{1}{2} y d y

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