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Popular >

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

Solution

derivative of

\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^{^{'}} - 2 t y = 4 t^{3}

integral from 4 to 5 of xsqrt(25-x^2)

\int_{4}^{5} x 25 - x^{2} d x

integral of (e^{-y})

\int (e^{- y}) d y

derivative of ((x-8))/(9x^2e^x)derivative of

\frac{( x - 8 )}{9 x ^{2} e ^{x}}

x^'=(1-x)*0.03-((0.03x))/((e^3-1))

x^{^{'}} = (1 - x) \cdot 0.03 - \frac{( 0.03 x )}{( e ^{3} - 1 )}

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})