en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arcsin(e^{-x})

Solution

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

Solution

- \frac{e ^{- x}}{1 - e ^{- 2 x}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

area y=ln(x),x=e,y=0 area

y = ln (x), x = e, y = 0

limit as x approaches-9 of 1-4x^3

x \to - 9 lim (1 - 4 x^{3})

integral from 0 to 5 of 2e^x

\int_{0}^{5} 2 e^{x} d x

limit as x approaches 2 of 3x^3+5x

x \to 2 lim (3 x^{3} + 5 x)

limit as x approaches pi/2 of 4sin(x)

x \to \frac{π}{2} lim (4 sin (x))

Frequently Asked Questions (FAQ)

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