What is the derivative of f(x)=x^{11}e^x ?

The derivative of f(x)=x^{11}e^x is 11x^{10}e^x+e^xx^{11}

What is the first derivative of f(x)=x^{11}e^x ?

The first derivative of f(x)=x^{11}e^x is 11x^{10}e^x+e^xx^{11}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

f (x) = x^{11} e^{x}

11 x^{10} e^{x} + e^{x} x^{11}

Solution steps

\frac{d}{d x} (x^{11} e^{x})

Apply the Product Rule:

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

f = x^{11}, g = e^{x}

= \frac{d}{d x} (x^{11}) e^{x} + \frac{d}{d x} (e^{x}) x^{11}

\frac{d}{d x} (x^{11}) = 11 x^{10}

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

= 11 x^{10} e^{x} + e^{x} x^{11}

What is the derivative of f(x)=x^{11}e^x ?
The derivative of f(x)=x^{11}e^x is 11x^{10}e^x+e^xx^{11}
What is the first derivative of f(x)=x^{11}e^x ?
The first derivative of f(x)=x^{11}e^x is 11x^{10}e^x+e^xx^{11}