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+e^{-x}/2)

Solution

\frac{d}{d x} (\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

y^{''}-10y^'+25y=0,y(0)=-3,y^'(0)=-29/2

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = - \frac{29}{2}

derivative of f(x)=-(13)/(x^4)derivative of

f (x) = - \frac{13}{x ^{4}}

integral from 0 to 6 of k(6-x)

\int_{0}^{6} k (6 - x)

inverse oflaplace (5(1-s^2))/((s+2)^3)inverse laplace

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

integral of ((2x+3))/((x+1)^2)

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

Frequently Asked Questions (FAQ)

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