Posted by **dino** on Monday, November 5, 2012 at 8:51pm.

Show that the tanget lines to the graph of Y= e^x - e^-x /e^x + e^-x at x =1 and x= -1 are parallel.

I know to use the Quotient rule but I am having a hard time with this problem.

- calculus -
**Steve**, Monday, November 5, 2012 at 9:17pm
y = tanh(x)

there are asymptotes at y=1 and y=-1

just consider when x gets large positive. e^-x vanishes, and you have e^x/e^x = 1

when x gets large negative, e^x vanishes, and you have -e^-x/e^-1 = -1

- calculus -
**Reiny**, Monday, November 5, 2012 at 9:30pm
first of all simplify it a bit,

multiplying top and bottom by e^x to get

y = (e^(2x) -1)/(e^(2x) + 1)

dy/dx = [(e^(2x) + 1)(2e^(2x)) - (e^(2x) -1)(2e^(2x)) )/(e^(2x) + 1)^2

= 2e^(2x)(e^(2x) + 1 + e^(2x) - 1)/(e^(2x+1)^2

= 4e^(2x)/(e^(2x)+1)^2

confirmed by Wolfram:

http://www.wolframalpha.com/input/?i=derivative+of+%28e^x+-+e^-x%29%2F%28e^x+%2B+e^-x%29

I will leave it up to you to sub in x=1 and x=-1 to show that you get the same value, I did.

- calculus -
**dino**, Monday, November 5, 2012 at 9:35pm
thank you very Much

## Answer this Question

## Related Questions

- Calculus - The graph of the equation x2 − xy + y2 = 9 is an ellipse. Find ...
- Calculus - Let f(x)= 5x ------- x–2 are we supposed to use the quotient rule? ...
- Calculus - How do I use the chain rule to find the derivative of square root(1-x...
- Calculus - f(x)=5+(6/x)+(7/x^2), find f'(x). I haven't done fractions without ...
- calculus - find one point on the graph of y= x+2cosx such that the tanget is ...
- Geometry - Solve for x 5/3 / 4/3 = x / 20/9 x= 25/9 =2.77777.... 5/4 = x/3 x= 15...
- Geometry - Solve for x x/6 = x+1 / 9 x= 2 Tell whether the lines are parallel ...
- geometry - Martin drew a pair of perpendicular lines and a pair of parallel ...
- Pre-Calculus - Let f(x) = [(√x)-7]/[(√x)+7]. What is f'(x)? What is ...
- 9th grade math - Hey i need help on my math hw i just dont get it lol please ...

More Related Questions