What's the derivative of tanh(x)?

We can write like that: tanh(x)=ex−e−xex+e−x So, we have: ddxtanh(x)=(ex+e−x)(ex+e−x)−(ex−e−x)(ex−e−x)(ex+e−x)2 =1−(ex−e−x)2(ex+e−x)2=1−tanh2(x)

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We can write like that: tanh(x)=ex−e−xex+e−x So, we have: ddxtanh(x)=(ex+e−x)(ex+e−x)−(ex−e−x)(ex−e−x)(ex+e−x)2 =1−(ex−e−x)2(ex+e−x)2=1−tanh2(x)

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Solved: "What's the derivative of tanh(x)?"

David Lewis

2021-12-09

What's the derivative of

tanh (x)

nghodlokl

Beginner2021-12-10Added 33 answers

We can write like that:

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

So, we have:

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

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

trisanualb6

Beginner2021-12-11Added 32 answers

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