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

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

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^2-y^2)})

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

x = 4 t^{2} - 3 t + 11

\frac{d}{d x} (sin^{2} (x) + sin (x))

4 cos (t)

x = 4 y^{2}, x = 2 + 2 y^{2}

\frac{\partial}{\partial x} (4 x^{2} + x y + 3 y^{2} - 8)

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