# Differentiate $y=((e^x)-(e^{-x}))/((e^x)+(e^{-x}))$  and   prove that $dy/dx=1-y^2$

Differentiate $y=((e^x)-(e^{-x}))/((e^x)+(e^{-x}))$  and   prove that $dy/dx=1-y^2$.

• Mathe

I think there is a typo in the question.

• Yap Guong Zer

There is no typo in the question, I'll try to rewrite to so that it is hopefully easier to understand basically it's e power of x minus e power of negative x over e power of x plus e power of negative x y=((e^x)-(e^-x))/((e^x)+(e^-x)) hope this helps

• Mathe

if y = ((e^x)-(e^-x))/((e^x)+(e^-x)), it is not true that y = 1 - y^2. Consider the case when x = 0. In that case y = 0.

• Yap Guong Zer

this is differentiation trying to prove that when y is differentiated, dy/dx=1-y^2. Are you saying that this is not achievable?

• Mathe

So there was a typo, because you didn't include dy/dx before

• Yap Guong Zer

ok, that was my bad , should have made it clearer, are you able to help with my quesrion now?

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• Yap Guong Zer