What is the derivative of 4e^{-x^2}x^3-6e^{-x^2}x ?

The derivative of 4e^{-x^2}x^3-6e^{-x^2}x is -8e^{-x^2}x^4+24e^{-x^2}x^2-6e^{-x^2}

What is the first derivative of 4e^{-x^2}x^3-6e^{-x^2}x ?

The first derivative of 4e^{-x^2}x^3-6e^{-x^2}x is -8e^{-x^2}x^4+24e^{-x^2}x^2-6e^{-x^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x)

- 8 e^{- x^{2}} x^{4} + 24 e^{- x^{2}} x^{2} - 6 e^{- x^{2}}

Solution steps

\frac{d}{d x} (4 e^{- x^{2}} x^{3} - 6 e^{- x^{2}} x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (4 e^{- x^{2}} x^{3}) - \frac{d}{d x} (6 e^{- x^{2}} x)

\frac{d}{d x} (4 e^{- x^{2}} x^{3}) = 4 (- 2 e^{- x^{2}} x^{4} + 3 e^{- x^{2}} x^{2})

\frac{d}{d x} (6 e^{- x^{2}} x) = 6 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}})

= 4 (- 2 e^{- x^{2}} x^{4} + 3 e^{- x^{2}} x^{2}) - 6 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}})

Simplify

4 (- 2 e^{- x^{2}} x^{4} + 3 e^{- x^{2}} x^{2}) - 6 (- 2 e^{- x^{2}} x^{2} + e^{- x^{2}}) : - 8 e^{- x^{2}} x^{4} + 24 e^{- x^{2}} x^{2} - 6 e^{- x^{2}}

= - 8 e^{- x^{2}} x^{4} + 24 e^{- x^{2}} x^{2} - 6 e^{- x^{2}}

y^{^{''}} + 36 y = 36 sin (6 x)

\int \frac{324 - x ^{2}}{x} d x

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

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

5 \frac{d y}{d t} + y = 20 t

What is the derivative of 4e^{-x^2}x^3-6e^{-x^2}x ?
The derivative of 4e^{-x^2}x^3-6e^{-x^2}x is -8e^{-x^2}x^4+24e^{-x^2}x^2-6e^{-x^2}
What is the first derivative of 4e^{-x^2}x^3-6e^{-x^2}x ?
The first derivative of 4e^{-x^2}x^3-6e^{-x^2}x is -8e^{-x^2}x^4+24e^{-x^2}x^2-6e^{-x^2}