What is the derivative of f(x)=(2x)/(e^x) ?

The derivative of f(x)=(2x)/(e^x) is (2(1-x))/(e^x)

What is the first derivative of f(x)=(2x)/(e^x) ?

The first derivative of f(x)=(2x)/(e^x) is (2(1-x))/(e^x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{2 x}{e ^{x}}

\frac{2 ( 1 - x )}{e ^{x}}

Solution steps

\frac{d}{d x} (\frac{2 x}{e ^{x}})

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

= 2 \cdot \frac{1 \cdot e ^{x} - e ^{x} x}{( e ^{x} ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot e ^{x} - e ^{x} x}{( e ^{x} ) ^{2}} : \frac{2 ( 1 - x )}{e ^{x}}

= \frac{2 ( 1 - x )}{e ^{x}}

n = 1 \sum \infty n! \cdot x^{n}

\frac{d}{d x} ((x + a) \cdot e^{2 x} + b)

f (x) = 4 sin^{2} (x)

\int - x^{2} d x

\int_{0}^{2} x 4 x^{2} + 9 d x

What is the derivative of f(x)=(2x)/(e^x) ?
The derivative of f(x)=(2x)/(e^x) is (2(1-x))/(e^x)
What is the first derivative of f(x)=(2x)/(e^x) ?
The first derivative of f(x)=(2x)/(e^x) is (2(1-x))/(e^x)