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

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

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

- 2 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- x^{2}}, g = x

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

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

\frac{\partial}{\partial x} (x) = 1

= - 2 ((- 2 e^{- x^{2}} x) x + 1 \cdot e^{- x^{2}})

Simplify

- 2 ((- 2 e^{- x^{2}} x) x + 1 \cdot e^{- x^{2}}) : - 2 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}})

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

\int 2 x - 6 x^{3} d x

- 5

x^{2}, 3 - 2 x

\frac{d y}{d x} = x y, y (0) = 1, y (1) = 2

\frac{d}{d x} (2 π - x cos (x))

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