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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Graph

Popular Examples

integral of e^{y^2}

\int e^{y^{2}} d y

integral of (10)/(sqrt(8x-4x^2))

\int \frac{10}{8 x - 4 x ^{2}} d x

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\int_{\frac{1}{2}}^{\frac{e}{2}} ln (2 x) d x

derivative of ((tan(x)-1))/(sec(x))derivative of

\frac{( tan ( x ) - 1 )}{sec ( x )}

derivative of (4x^2+9^6)

\frac{d}{d x} ((4 x^{2} + 9)^{6})

Frequently Asked Questions (FAQ)

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