[RyanGT]

Can anybody help me out? doing a stupid math project and this would quicken it up!

Need to find the derivative of the profit function p(t)= 10,000(6.7e^(48.1/t)) - 200t + 1000.

P '(t) = ?

[AtlanticBlue99]

review derivatives law of logs and natural logs. the rest is cake.

[dude496]

sorry i'm no help lol

[AnimalCrackers]

derivative of the function e is just that function times the derivative of the exponent.

p'=10,000*6.7*-48.1/t^2 * e^(48.1/t) - 200

[RyanGT]

Yeah im looking at the log section now. The back portion of the function is easy. And i should of simplified the first portion to 67000E^(blah blah). doesnt look as bad now.

Ill see what i can get. Think you could check answer once i get it? (or anybody).

[RyanGT]

thanks Animal! Your the man. im not i posted other response slow

[GreenFaleen]

you need to use the product rule, the chain rule, and the quotient rule, remember the derivative of e^a is e^a*(da/dx)

example:
d/dx of e^(x^2) = e^(x^2)*2x

[BWAL]

Originally Posted by dude496 sorry i'm no help lol

[AnimalCrackers]

Originally Posted by GreenFaleen you need to use the product rule, the chain rule, and the quotient rule, remember the derivative of e^a is e^a*(da/dx) example: d/dx of e^(x^2) = e^(x^2)*2x

it's been a few years since calculus, but it's just a simple substitution:
u=48.1/t
du=-48.1/t^2

d/dx e^u=e^u * du

everything else is just a constant, addition, or multiplier.

[White99stang]

i used to be really good at that, but then realized its all worthless and its not needed in the real world, haven't used a single bit of anything besides basic math since i have been working.

[GreenFaleen]

Originally Posted by AnimalCrackers it's been a few years since calculus, but it's just a simple substitution: u=48.1/t du=-48.1/t^2 d/dx e^u=e^u * du everything else is just a constant, addition, or multiplier.

for e thats correct but for the rest of the function he has to use the product rule on the first part and then the chain rule on the e section as well as the quotient rule for the power e is raised to

[RyanGT]

Im so lost now green! Could you try it out real quick? I just threw the equation in excel and its funky so i think your right.

And you could just multiply the 10000 to 6.7E, i didnt simplify it all the way before i posted (didn't notice).

[GreenFaleen]

you could but it is harder if you do h/o ill figure it out for ya

[RyanGT]

Ok thanks a lot dude! Im not the greatest at calc (second time in class) and its online so no lectures. Stats/accting type math is cake for me though!

[GreenFaleen]

it is
((-3.2227*10^6*(7.75469*10^20)^(1/t))/t^2)-200

np i suck at calc too 4th time in the class lol I get derivative and integration is optimization that kills me)

[RyanGT]

where did the e go? did you change it to 2.718 ?

[GreenFaleen]

nope it canceled out I think I just put it in my calculator

[RyanGT]

Oh ok! Wonder how ill bs to show my work hehe. Think you could give me a midway step? (i know you dont want to do calculus). You should probably be doing your paper haha!

[GreenFaleen]

Originally Posted by RyanGT Oh ok! Wonder how ill bs to show my work hehe. Think you could give me a midway step? (i know you dont want to do calculus). You should probably be doing your paper haha!

multiply out 10000*e^(whatever it is) then do the quotent rule

then use the product rule, then chin in the e then chain in the derivitive of what e is raised to where you use the quotent rule

[RyanGT]

Ok ill see if i can come up with something.

What did you type into your calc? I have to change the function a little bit later with a price change. I don't remember how to get derivatives without the limits.