# solve for me this question please..

• Sep 16th 2012, 09:37 AM
sharmala
solve for me this question please..
hi..can anyone please solve for me this qjuestion...Given that y=e^x - e^-x/e^x + e^-x , show that dy/dx=1-y​^2.thank u
• Sep 16th 2012, 10:27 AM
skeeter
Re: solve for me this question please..
Quote:

Originally Posted by sharmala
hi..can anyone please solve for me this qjuestion...Given that y=e^x - e^-x/e^x + e^-x , show that dy/dx=1-y​^2.thank u

$y= \frac{e^x - e^{-x}}{e^x + e^{-x}}$

so, what do you get for dy/dx using the quotient rule?

fyi, calculus questions belong in the calculus forum. also, please using grouping symbols (parentheses) to make clear your expressions.
• Sep 16th 2012, 09:12 PM
Prove It
Re: solve for me this question please..
Quote:

Originally Posted by sharmala
hi..can anyone please solve for me this qjuestion...Given that y=e^x - e^-x/e^x + e^-x , show that dy/dx=1-y​^2.thank u

Notice that \displaystyle \begin{align*} \frac{e^x - e^{-x}}{e^x + e^{-x}} = \tanh{x} \end{align*}. So we have

\displaystyle \begin{align*} y &= \tanh{x} \\ \frac{dy}{dx} &= \textrm{sech}^2\,{x} \\ &= 1 - \tanh^2{x} \\ &= 1 - y^2 \end{align*}