What is the derivative of g(x)=6x^2e^{-x} ?

The derivative of g(x)=6x^2e^{-x} is 6(2e^{-x}x-e^{-x}x^2)

What is the first derivative of g(x)=6x^2e^{-x} ?

The first derivative of g(x)=6x^2e^{-x} is 6(2e^{-x}x-e^{-x}x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

g (x) = 6 x^{2} e^{- x}

6 (2 e^{- x} x - e^{- x} x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= 6 (2 e^{- x} x - e^{- x} x^{2})

What is the derivative of g(x)=6x^2e^{-x} ?
The derivative of g(x)=6x^2e^{-x} is 6(2e^{-x}x-e^{-x}x^2)
What is the first derivative of g(x)=6x^2e^{-x} ?
The first derivative of g(x)=6x^2e^{-x} is 6(2e^{-x}x-e^{-x}x^2)