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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= e^{- x^{2} - y^{2}} (- 2 y)

Simplify

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

x \to 3 lim (\frac{tan ( x - 3 )}{3 e ^{x - 3} - x})

\frac{1}{x ^{2} + 4}

\frac{d}{d x} (x^{7} ln (8 x))

\frac{d}{d x} (\frac{tan ( x )}{x ^{2}})

f (x) = \frac{4 x}{x + 3}, (1, 1)

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