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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

integral of (6e^{5x}-7/x)

\int (6 e^{5 x} - \frac{7}{x}) d x

derivative of (6x-3/(x-3))

\frac{d}{d x} (\frac{6 x - 3}{x - 3})

integral of sin(6t)

\int sin (6 t) d t

derivative of (sin(0.5sqrt(x))/x)

\frac{d}{d x} (\frac{sin ( 0.5 x )}{x})

integral of-(2000x)/((1+x^2))

\int - \frac{2000 x}{( 1 + x ^{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})