What is the derivative of (x^5/(e^x)) ?

The derivative of (x^5/(e^x)) is (x^4(5-x))/(e^x)

What is the first derivative of (x^5/(e^x)) ?

The first derivative of (x^5/(e^x)) is (x^4(5-x))/(e^x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{x ^{4} ( 5 - x )}{e ^{x}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{5} ) e ^{x} - \frac{d}{d x} ( e ^{x} ) x ^{5}}{( e ^{x} ) ^{2}}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= \frac{5 x ^{4} e ^{x} - e ^{x} x ^{5}}{( e ^{x} ) ^{2}}

Simplify

\frac{5 x ^{4} e ^{x} - e ^{x} x ^{5}}{( e ^{x} ) ^{2}} : \frac{x ^{4} ( 5 - x )}{e ^{x}}

= \frac{x ^{4} ( 5 - x )}{e ^{x}}

What is the derivative of (x^5/(e^x)) ?
The derivative of (x^5/(e^x)) is (x^4(5-x))/(e^x)
What is the first derivative of (x^5/(e^x)) ?
The first derivative of (x^5/(e^x)) is (x^4(5-x))/(e^x)