What is the derivative of (2e^x/(5x)) ?

The derivative of (2e^x/(5x)) is (2(e^xx-e^x))/(5x^2)

What is the first derivative of (2e^x/(5x)) ?

The first derivative of (2e^x/(5x)) is (2(e^xx-e^x))/(5x^2)

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{2 e ^{x}}{5 x})

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d y}{d t} + e^{t} y = 22 e^{t}

\int sin (2 θ) cos^{4} (2 θ) d θ

\int \frac{1}{sec ( θ )} d θ

\frac{d}{d t} (t cos (t))

cos (5 t) + sin (2 t)

What is the derivative of (2e^x/(5x)) ?
The derivative of (2e^x/(5x)) is (2(e^xx-e^x))/(5x^2)
What is the first derivative of (2e^x/(5x)) ?
The first derivative of (2e^x/(5x)) is (2(e^xx-e^x))/(5x^2)