en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^{3/x}

Solution

derivative of

e^{\frac{3}{x}}

Solution

- \frac{3 e ^{\frac{3}{x}}}{x ^{2}}

Solution steps

\frac{d}{d x} (e^{\frac{3}{x}})

Apply the chain rule:

e^{\frac{3}{x}} \frac{d}{d x} (\frac{3}{x})

= e^{\frac{3}{x}} \frac{d}{d x} (\frac{3}{x})

\frac{d}{d x} (\frac{3}{x}) = - \frac{3}{x ^{2}}

= e^{\frac{3}{x}} (- \frac{3}{x ^{2}})

Simplify

e^{\frac{3}{x}} (- \frac{3}{x ^{2}}) : - \frac{3 e ^{\frac{3}{x}}}{x ^{2}}

= - \frac{3 e ^{\frac{3}{x}}}{x ^{2}}

Popular Examples

y^{''}-y=(2e^{-x})/((1+e^{-2x))^2}

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

(dy)/(dx)+(xy)/(x^2+1)= x/(x^2+1)

\frac{d y}{d x} + \frac{x y}{x ^{2} + 1} = \frac{x}{x ^{2} + 1}

limit as n approaches infinity of-3^{-n}

n \to \infty lim (- 3^{- n})

integral of 1/(sqrt(x+1))

\int \frac{1}{x + 1} d x

tangent of f(x)=8+4x^2-2x^3,\at x=2 tangent of

f (x) = 8 + 4 x^{2} - 2 x^{3}, at x = 2

Frequently Asked Questions (FAQ)

What is the derivative of e^{3/x} ?
The derivative of e^{3/x} is -(3e^{3/x})/(x^2)
What is the first derivative of e^{3/x} ?
The first derivative of e^{3/x} is -(3e^{3/x})/(x^2)