en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (5x/(e^x))

Solution

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

Solution

\frac{5 ( 1 - x )}{e ^{x}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

= 5 \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}

= 5 \cdot \frac{1 \cdot e ^{x} - e ^{x} x}{( e ^{x} ) ^{2}}

Simplify

5 \cdot \frac{1 \cdot e ^{x} - e ^{x} x}{( e ^{x} ) ^{2}} : \frac{5 ( 1 - x )}{e ^{x}}

= \frac{5 ( 1 - x )}{e ^{x}}

Popular Examples

derivative of arcsin(x/(1+x^2))

\frac{d}{d x} (arcsin (\frac{x}{1 + x ^{2}}))

derivative of ((2pi-xcos(x))/(x-2pi))

\frac{d}{d x} (\frac{( 2 π - x cos ( x ) )}{x - 2 π})

expand ((3x^2-4)(x^2-6))/(x^2+4)expand

\frac{( 3 x ^{2} - 4 ) ( x ^{2} - 6 )}{x ^{2} + 4}

(\partial)/(\partial y)(x/(y+x))

\frac{\partial}{\partial y} (\frac{x}{y + x})

derivative of (x^2+3^{sin(x)})

\frac{d}{d x} ((x^{2} + 3)^{s i n (x)})

Frequently Asked Questions (FAQ)

What is the derivative of (5x/(e^x)) ?
The derivative of (5x/(e^x)) is (5(1-x))/(e^x)
What is the first derivative of (5x/(e^x)) ?
The first derivative of (5x/(e^x)) is (5(1-x))/(e^x)