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 $dy/dx=1-y^2$.
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
Mathe
3.7K
-
thank you very much
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 789 views
- $5.00
Related Questions
- Linearization of nonlinear differential equations near an equilibrium position
- Leaky Buckets: Volume in a system of 2+ buckets that can be empty
- Solve the initial value problem $(\cos y )y'+(\sin y) t=2t$ with $y(0)=1$
- Ordinary differential equation questions
- Find the general solution of the system of ODE $X'=\begin{bmatrix} 1 & 3 \\ -3 & 1 \end{bmatrix} X$
- Differentai equations, question 2.
- Burgers’ equation $u_t + u u_x = −x $
- Aysomptotical stability
I think there is a typo in the question.
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
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.
this is differentiation trying to prove that when y is differentiated, dy/dx=1-y^2. Are you saying that this is not achievable?
So there was a typo, because you didn't include dy/dx before
ok, that was my bad , should have made it clearer, are you able to help with my quesrion now?