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

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

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Answer 1 · 2016-11-02T01:57:31

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

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