f(x) = cosh^2(x)+sinh(2x) = y(adsbygoogle = window.adsbygoogle || []).push({});

f'(x) = sinh(2x)+2cosh(2x) = 3e^(2x) + e^(-x) = y'

Let g(y) be the inverse of f(x):

g'(y) = 1 / f'(x) = 1 / [3e^(2y) + e^(-2y)] = e^(2y) / [4e^(2y) + 1]

Integrating gives: [ 3^(1/2)/3 ]*arctan[ 3^(1/2) * e^(2y) ] + C

Now when I plotted this function it looked in no way like the inverse of f(x), so where have I gone wrong?

Thank you

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# Derivative of an inverse function

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