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Popular >

d/(dy)((e^y+e^{-y})/2)

Solution

\frac{d}{d y} (\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})

Popular Examples

y^{''}-2y^'+3y=0

y^{^{''}} - 2 y^{^{'}} + 3 y = 0

derivative of 1/3 sin^3(x-sin(x)+1)

\frac{d}{d x} (\frac{1}{3} sin^{3} (x) - sin (x) + 1)

limit as x approaches 4 of (x+4)/(x+7)

x \to 4 lim (\frac{x + 4}{x + 7})

(\partial)/(\partial x)(e^{-2x}cos(6y))

\frac{\partial}{\partial x} (e^{- 2 x} cos (6 y))

limit as x approaches sqrt(x) of 25

x \to x lim (25)

Frequently Asked Questions (FAQ)

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