en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of e^{-x}*ln(x)

Solution

\frac{d}{d x} (e^{- x} \cdot ln (x))

Solution

- e^{- x} ln (x) + \frac{e ^{- x}}{x}

Solution steps

\frac{d}{d x} (e^{- x} ln (x))

Apply the Product Rule:

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

f = e^{- x}, g = ln (x)

= \frac{d}{d x} (e^{- x}) ln (x) + \frac{d}{d x} (ln (x)) e^{- x}

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

Simplify

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

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

Popular Examples

tangent of y=2x^3-3x,(1,-1)tangent of

y = 2 x^{3} - 3 x, (1, - 1)

4sqrt(xy)((dy)/(dx))=3

4 x y (\frac{d y}{d x}) = 3

limit as x approaches 0 of b+0^c*ln(0)

x \to 0 lim (b + 0^{c} \cdot ln (0))

limit as k approaches infinity of 2k+1

k \to \infty lim (2 k + 1)

integral from 0 to 4 of (16-x^2)

\int_{0}^{4} (16 - x^{2}) d x

Frequently Asked Questions (FAQ)

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