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

The derivative of e^{-arcsinh(x/2}) is -(e^{-arcsinh(x/2)})/(sqrt(x^2+4))

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

The first derivative of e^{-arcsinh(x/2}) is -(e^{-arcsinh(x/2)})/(sqrt(x^2+4))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

- \frac{e ^{- arcsinh (\frac{x}{2})}}{x ^{2} + 4}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (- arcsinh (\frac{x}{2})) = - \frac{1}{x ^{2} + 4}

= e^{- arcsinh (\frac{x}{2})} (- \frac{1}{x ^{2} + 4})

Simplify

e^{- arcsinh (\frac{x}{2})} (- \frac{1}{x ^{2} + 4}) : - \frac{e ^{- arcsinh (\frac{x}{2})}}{x ^{2} + 4}

= - \frac{e ^{- arcsinh (\frac{x}{2})}}{x ^{2} + 4}

\frac{x}{6 x - 6}

\frac{d}{d x} (∣ x ∣^{3})

\int \frac{1}{( 4 x - x ^{2} ) ^{3}} d x

\int e^{- t (a + s)} d t

\int_{50}^{50.25} 2 d x

What is the derivative of e^{-arcsinh(x/2}) ?
The derivative of e^{-arcsinh(x/2}) is -(e^{-arcsinh(x/2)})/(sqrt(x^2+4))
What is the first derivative of e^{-arcsinh(x/2}) ?
The first derivative of e^{-arcsinh(x/2}) is -(e^{-arcsinh(x/2)})/(sqrt(x^2+4))