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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})

Popular Examples

integral of (x^2-9)/(x-3)

\int \frac{x ^{2} - 9}{x - 3} d x

derivative of (x^3+1^{1/3})

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

(\partial)/(\partial {K)}(-sqrt(2{K)^2+L^2})

\frac{\partial}{\partial K} (- 2 K^{2} + L^{2})

integral of (2x-1)/(sqrt(x^2-7))

\int \frac{2 x - 1}{x ^{2} - 7} d x

(\partial)/(\partial x)(zy)

\frac{\partial}{\partial x} (zy)

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})