What is (\partial}{\partial x}(\frac{e^x-e^{-x})/2) ?

The answer to (\partial}{\partial x}(\frac{e^x-e^{-x})/2) is 1/2 (e^x+e^{-x})

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(\partial}{\partial x}(\frac{e^x-e^{-x})/2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (e^{x}) = e^{x}

\frac{\partial}{\partial x} (e^{- x}) = - e^{- x}

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

Simplify

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

\frac{1}{u}

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

\frac{\partial}{\partial x} (42 y^{9} x^{5} - 30 y^{8} x^{4})

\int \frac{x ^{2} - 4 x - 4}{x ^{3} - 2 x ^{2} + 4 x - 8} d x

x \to 3 lim (12 - 4 x + 2)

What is (\partial}{\partial x}(\frac{e^x-e^{-x})/2) ?
The answer to (\partial}{\partial x}(\frac{e^x-e^{-x})/2) is 1/2 (e^x+e^{-x})