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Popular >

derivative of (e^x+e^{-x}/9)

Solution

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{9})

Solution

\frac{1}{9} (e^{x} - e^{- x})

Solution steps

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{9})

Take the constant out:

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

= \frac{1}{9} \frac{d}{d x} (e^{x} + e^{- x})

Apply the Sum/Difference Rule:

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

= \frac{1}{9} (\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}{9} (e^{x} - e^{- x})

Graph

Popular Examples

implicit x^{2/3}+y^{2/3}=4 implicit derivative

x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4

integral of (x^2+x)

\int (x^{2} + x) d x

(\partial)/(\partial t)(sqrt(t))

\frac{\partial}{\partial t} (t)

(\partial)/(\partial x)(ln(y-x))

\frac{\partial}{\partial x} (ln (y - x))

derivative of (x^6/(2-x^5))

\frac{d}{d x} (\frac{x ^{6}}{2 - x ^{5}})

Frequently Asked Questions (FAQ)

What is the derivative of (e^x+e^{-x}/9) ?
The derivative of (e^x+e^{-x}/9) is 1/9 (e^x-e^{-x})
What is the first derivative of (e^x+e^{-x}/9) ?
The first derivative of (e^x+e^{-x}/9) is 1/9 (e^x-e^{-x})