en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=(e^x+e^{-x})/2

Solution

derivative of

y = \frac{e ^{x} + e ^{- x}}{2}

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Popular Examples

f (x) = e^{1 - x}

integral of x^2arctan(7x)

\int x^{2} arctan (7 x) d x

integral of 1/(sqrt(1-4x^2))

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

d/(d{r)}((({r}^2-1)^3)/((2{r)+1)^5})

\frac{d}{d r} (\frac{( r ^{2} - 1 ) ^{3}}{( 2 r + 1 ) ^{5}})

integral from 4 to 6 of (x^2+2x-8)

\int_{4}^{6} (x^{2} + 2 x - 8) d x

Frequently Asked Questions (FAQ)

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