en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=x^3e^{-8x}

Solution

derivative of

y = x^{3} e^{- 8 x}

Solution

3 e^{- 8 x} x^{2} - 8 e^{- 8 x} x^{3}

Solution steps

\frac{d}{d x} (x^{3} e^{- 8 x})

Apply the Product Rule:

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

f = x^{3}, g = e^{- 8 x}

= \frac{d}{d x} (x^{3}) e^{- 8 x} + \frac{d}{d x} (e^{- 8 x}) x^{3}

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

\frac{d}{d x} (e^{- 8 x}) = - 8 e^{- 8 x}

= 3 x^{2} e^{- 8 x} + (- 8 e^{- 8 x}) x^{3}

Simplify

= 3 e^{- 8 x} x^{2} - 8 e^{- 8 x} x^{3}

Graph

Popular Examples

(\partial)/(\partial y)((9y)/(x^3))

\frac{\partial}{\partial y} (\frac{9 y}{x ^{3}})

integral of 0.5e^{-x}

\int 0.5 e^{- x} d x

integral of 4/((x^2+1)^{3/2)}

\int \frac{4}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

derivative of (x^5/(x^3))

\frac{d}{d x} (\frac{x ^{5}}{x ^{3}})

limit as x approaches 9 of [f(18)-g(7)]

x \to 9 lim ([f (18) - g (7)])

Frequently Asked Questions (FAQ)

What is the derivative of y=x^3e^{-8x} ?
The derivative of y=x^3e^{-8x} is 3e^{-8x}x^2-8e^{-8x}x^3
What is the first derivative of y=x^3e^{-8x} ?
The first derivative of y=x^3e^{-8x} is 3e^{-8x}x^2-8e^{-8x}x^3