I need a couple of derivatives

1.
12.921e^-0.26578x
FIND THE DERIVATIVE
2.
(97)/(1+311e^-0.68x)
FIND THE DERIVATIVE
thanks!!!

 

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Well, I;m not sure on this because I haven't done derivates in ages but I believe taking derivates in this case :

if
y = e^x then

y' = x'e^x

by that convention 1) equals: 12.921(-0.26578)e^-0.26578x = 3.434e^-0.26578x

For 2) when taking derivates of fractions you could use quiotent rule or modifity to use the chain rule. I usually do the latter when I can.

So (97)/(1+311e^-0.68x) becomes (97)*(1+311e^-.68x)^-1

then using the chain rule:

0 + (97)*-(1+311e^1+311e^-.68x)^-2*(-211.48e^-.68x) and then simlify the equation.

Now I am just doing these from what I remember. Please do not think these answers are completely correct. Make sure you check them. Hopefully I helped you out.

 

This thread made me throw up in my mouth. I hate this stuff! However, if you don't get the help you need I'll look in my old business math textbook when I get home to see if I can help you out.

 

TI-89 ftw

 

He meant the product rule, not the chain rule.

(Mind you, he's using the chain rule for both computations, but the effect of rewriting the quotient as a product was that he could use the product rule instead of the quotient rule. I suspect that he forgets which term is positive and which negative in the quotient rule; many people do.)

 

This is true but the answers are correct nonetheless! A quotient can always be looked at as a product e.g. A/B = A*1/B and since the quotient rule is slightly more complicated than the product rule so we prefer the product rule approach ofcourse. The chain rule is for when you have a function such as h(x) = g(f(x)) e.g. e^(x^2).

 

 

 

I wasn't suggesting that the answers were incorrect. I simply pointed out that the author misnamed the rule he sought to use.

I'm not sure who constitutes "we" in those who prefer to rewrite quotients as products and use the product rule instead of the quotient rule. I've been teaching calculus for over twenty years; neither I nor any other calculus instructor I know falls into that set.