What is the derivative of ln(e^x+e^{-x}) ?

The derivative of ln(e^x+e^{-x}) is (e^{2x}-1)/(e^{2x)+1}

What is the first derivative of ln(e^x+e^{-x}) ?

The first derivative of ln(e^x+e^{-x}) is (e^{2x}-1)/(e^{2x)+1}

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Popular >

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 4 + lim (\frac{2}{( x - 4 ) ^{4}})

16 y^{^{''''}} = 256 y

\int ln (1 + \frac{1}{x ^{2}}) d x

\int (3 x + 1)^{\frac{1}{2}} d x

\frac{d}{d x} ((3 - 2 x)^{2})

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