What is the derivative of x^4(e^x) ?

The derivative of x^4(e^x) is 4x^3e^x+e^xx^4

What is the first derivative of x^4(e^x) ?

The first derivative of x^4(e^x) is 4x^3e^x+e^xx^4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

x^{4} (e^{x})

4 x^{3} e^{x} + e^{x} x^{4}

Solution steps

\frac{d}{d x} (x^{4} e^{x})

Apply the Product Rule:

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

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

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

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

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

= 4 x^{3} e^{x} + e^{x} x^{4}

What is the derivative of x^4(e^x) ?
The derivative of x^4(e^x) is 4x^3e^x+e^xx^4
What is the first derivative of x^4(e^x) ?
The first derivative of x^4(e^x) is 4x^3e^x+e^xx^4