What is the derivative of (6x/(e^x)) ?

The derivative of (6x/(e^x)) is (6(1-x))/(e^x)

What is the first derivative of (6x/(e^x)) ?

The first derivative of (6x/(e^x)) is (6(1-x))/(e^x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{6 x}{e ^{x}})

\frac{6 ( 1 - x )}{e ^{x}}

Solution steps

\frac{d}{d x} (\frac{6 x}{e ^{x}})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{x}{e ^{x}})

Apply the Quotient Rule:

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

= 6 \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}

= 6 \cdot \frac{1 \cdot e ^{x} - e ^{x} x}{( e ^{x} ) ^{2}}

Simplify

6 \cdot \frac{1 \cdot e ^{x} - e ^{x} x}{( e ^{x} ) ^{2}} : \frac{6 ( 1 - x )}{e ^{x}}

= \frac{6 ( 1 - x )}{e ^{x}}

\int x^{2} cos (w x) d x

f (I) = \frac{110 I}{I ^{2} + I + 1}

arctan (4 t)

\int \frac{x ^{2}}{3 - x ^{3}} d x

1500 x + 3000 (5 x + 3)^{- 1} - 1000

What is the derivative of (6x/(e^x)) ?
The derivative of (6x/(e^x)) is (6(1-x))/(e^x)
What is the first derivative of (6x/(e^x)) ?
The first derivative of (6x/(e^x)) is (6(1-x))/(e^x)