How do you find the derivative of y = tanh^-1 (1/x)?

1 Answer
Steve M
Nov 2, 2016

dy/dx=1/(1-x^2)

Explanation:

y=tanh^-1(1/x) => tanhy=1/x

Differentiating implicitly gives:

(1-tanh^2y)dy/dx=-1/x^2
:. (1-(1/x)^2)dy/dx=-1/x^2
:. dy/dx=-1/((x^2)(1-(1/x)^2))
:. dy/dx=-1/((x^2)(1-1/x^2))
:. dy/dx=-1/(x^2-1)
:. dy/dx=1/(1-x^2)

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