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

The derivative of 2*x*e^{-4*x^3} is 2(e^{-4x^3}-12e^{-4x^3}x^3)

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

The first derivative of 2*x*e^{-4*x^3} is 2(e^{-4x^3}-12e^{-4x^3}x^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

2 \cdot x \cdot e^{- 4 \cdot x^{3}}

2 (e^{- 4 x^{3}} - 12 e^{- 4 x^{3}} x^{3})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{- 4 x^{3}}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{- 4 x^{3}}) = - 12 e^{- 4 x^{3}} x^{2}

= 2 (1 \cdot e^{- 4 x^{3}} + (- 12 e^{- 4 x^{3}} x^{2}) x)

Simplify

2 (1 \cdot e^{- 4 x^{3}} + (- 12 e^{- 4 x^{3}} x^{2}) x) : 2 (e^{- 4 x^{3}} - 12 e^{- 4 x^{3}} x^{3})

= 2 (e^{- 4 x^{3}} - 12 e^{- 4 x^{3}} x^{3})

What is the derivative of 2*x*e^{-4*x^3} ?
The derivative of 2*x*e^{-4*x^3} is 2(e^{-4x^3}-12e^{-4x^3}x^3)
What is the first derivative of 2*x*e^{-4*x^3} ?
The first derivative of 2*x*e^{-4*x^3} is 2(e^{-4x^3}-12e^{-4x^3}x^3)