Derivative of Hyperbolic Trigonometric Function

[gurtaj]

Homework Statement

derivative of (e^x-e^-x)/(e^x+e^-x)

Homework Equations

The Attempt at a Solution

This answer was marked 2/4 on the test, can anyone help me get the right answer please ?

 

[micromass]

Hi gurtaj!

I don't understand your first step: you have $(e^x-e^{-x})(e^x+e^{-x})^{-1}$ and you wish to derive it. The product rule says that this equals

$$(e^x-e^{-x})^\prime(e^x+e^{-x})^{-1}+(e^x-e^{-x})((e^x+e^{-x})^{-1})^\prime$$

You did the second part of the sum allright, but you didn't differentiate anything in the first part of the sum...

 

[gurtaj]

oh sorry the next step after
$(e^x-e^{-x})(e^x+e^{-x})^{-1}$
I meant to put
$(e^x+e^{-x}) (e^x+e^{-x})^{-1} + (e^x-e^{-x})(-1)(e^x+e^{-x})^{-2}(e^x-e^{-x})$

so i did
derivative of the first one times second , then derivative of the second one times first

 

[micromass]

OK, so that expression will evaluate easily to the answer...

 

[gurtaj]

i think that is right too but somehow it was marked 2/4, and the teacher wrote expand and simplify

 

[micromass]

Yes, the final answer is correct. But if I was your teacher I would have given 2/4 too. The point is that your notation is really messy and you can't really see what you're doing And you're making the problem longer than it needs to be...

 

[gb7nash]

Quotient rule will greatly simplify your answer, and be much cleaner.

 

[gurtaj]

Yes, the final answer is correct. But if I was your teacher I would have given 2/4 too. The point is that your notation is really messy and you can't really see what you're doing And you're making the problem longer than it needs to be...

The teacher didn't cut 2 marks for messy notations or making the problem longer, she said its the answer that's wrong. She said you can expand that answer even more

 

[gurtaj]

I tried Quotient rule and end up with same answer

$(e^x-e^{-x})/(e^x+e^{-x})$

$(e^x+e^{-x}) (e^x+e^{-x})-(e^x-e^{-x})(e^x-e^{-x})/ (e^x+e^{-x})^{2}$

$1-((e^x-e^{-x})^{2}/ (e^x+e^{-x})^{2})$

 

[micromass]

Then I guess your teacher wants you to simplify your answer. Put your fractions on one denominator and work out the squares...
A bit silly to subtract points for that, unless she stated that your answer must be simplified...

 

[gb7nash]

She said you can expand that answer even more

Ohhhh, I see what's going on here.

Hint: Look and sinh and cosh.

You still the problem right though. I can't see why your teacher would give you half credit.

(Also, look at tanh)

 

[gurtaj]

Ohhhh, I see what's going on here.

Hint: Look and sinh and cosh.

You still the problem right though. I can't see why your teacher would give you half credit.

(Also, look at tanh)

We never learned Hyperbolic function, so she wasn't expecting that from us

 

[gb7nash]

I have no idea then. I think your instructor's crazy.

 

[micromass]

I have no idea then. I think your instructor's crazy.

I second that!