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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}))

Simplify

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

Popular Examples

d/(d{x)}(({x})/(({x)^2+{y}^2+{z}^2)^{3/2}})

\frac{d}{d x} (\frac{x}{( x ^{2} + y ^{2} + z ^{2} ) ^{\frac{3}{2}}})

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

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

limit as x approaches-infinity of x-(x)

x \to - \infty lim (x - (x))

y d x - x d y = 0

integral from 2 to 5 of x

\int_{2}^{5} x 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})