What is the derivative of (x+2)e^{1/x} ?

The derivative of (x+2)e^{1/x} is e^{1/x}-(e^{1/x}(x+2))/(x^2)

What is the first derivative of (x+2)e^{1/x} ?

The first derivative of (x+2)e^{1/x} is e^{1/x}-(e^{1/x}(x+2))/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + 2, g = e^{\frac{1}{x}}

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

\frac{d}{d x} (x + 2) = 1

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

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

Simplify

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

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

\int_{- 2}^{0} x^{2} + x - 1 d x

x \to 0 lim (\frac{( tan ( 2 x ) )}{x})

7 x + 1

\frac{d}{d x} (6 arcsinh (tan (x)))

\frac{\partial}{\partial x} (ln (6 x^{2} - 4 y^{2}))

What is the derivative of (x+2)e^{1/x} ?
The derivative of (x+2)e^{1/x} is e^{1/x}-(e^{1/x}(x+2))/(x^2)
What is the first derivative of (x+2)e^{1/x} ?
The first derivative of (x+2)e^{1/x} is e^{1/x}-(e^{1/x}(x+2))/(x^2)