Derivative of 14x/(1+12.6e^(-0.73x)

Hello, I'm having some brain freeze on finding the derivative for this problem.

First, I changed the denominator to , and then used the Product Rule.

That left me with:

This is where I'm getting brain frozen. I checked the back off the book it says the answer is: .

I'm not sure where the value of came from. I see parts of the Chain Rule, but the 128.772 has me dumbfounded. If there's a coefficient in front of what happens when taking the derivative of ?

Re: Derivative of 14x/(1+12.6e^(-0.73x)

Sorry about my handwriting

http://i.imgur.com/lEOEG.png

The last step I just used the distributive property

Re: Derivative of 14x/(1+12.6e^(-0.73x)

During your step here:

You should show how you used the Chain Rule to see where you made the error, since you never finished the Chain rule on the second term's

Re: Derivative of 14x/(1+12.6e^(-0.73x)

If you feel insistent about the Product rule:

http://i.imgur.com/XjbCy.png

I thought this might not be clear enough and I was going to make some changes but it's late and I have to sleep so bye for now

Re: Derivative of 14x/(1+12.6e^(-0.73x)

Hello, AZach!

The derivative of: .

. . . . . . . . . . .is: .

. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . .

Unless you are *very* good at handling negative exponents,

. . I do *not* recommend switching to the Product Rule.

Re: Derivative of 14x/(1+12.6e^(-0.73x)

Re: Derivative of 14x/(1+12.6e^(-0.73x)

Quote:

Originally Posted by

**AZach** Looking at this from a function point of view, is

and

both considered inside functions of

?

Absolutely - it's a glass-onion / russian doll situation!

Just in case a picture helps...

http://www.ballooncalculus.org/draw/diffChain/nest4.png

... where (key in spoiler) ...

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