"Find the derivative of the following functions y=ln⁡(ex+e−x)" was answered by our community

FobelloE

Answered question

2021-10-09

Find the derivative of the following functions

y = \ln (e^{x} + e^{- x})

Answer & Explanation

Nathalie Redfern

Skilled2021-10-10Added 99 answers

Step 1

y = \ln (e^{x} + e^{- x})

Take derivative both side,

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

Step 2

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

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

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

\frac{d y}{d x} = \frac{e^{x} - e^{- x}}{e^{x} + e^{- x}}

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