first and second derivatives of these equations

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first and second derivatives of these equations

Postby doodoo21 on Tue Aug 24, 2010 5:27 am

Hi Guys,

I'm having trouble working out some equations mostly dealing with exponential and logs.

the equations are:

y= 2x + 3^(-12x)

y= x^(-2x) - (e^2x)/5

I need to find both the first and second derivative. Any help and explanation would be much appreciated.

Thanks guys.
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Postby stapel_eliz on Tue Aug 24, 2010 10:54 am

doodoo21 wrote:y= 2x + 3^(-12x)

y= x^(-2x) - (e^2x)/5

I need to find both the first and second derivative.

Where are you getting stuck?

Please be complete. Thank you! :wink:
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Re:

Postby doodoo21 on Tue Aug 24, 2010 3:37 pm

stapel_eliz wrote:
doodoo21 wrote:y= 2x + 3^(-12x)

y= x^(-2x) - (e^2x)/5

I need to find both the first and second derivative.

Where are you getting stuck?

Please be complete. Thank you! :wink:


From my understanding the first one has to do with ln

so dy/dx = 2 - 12ln3(3^-12x)

I'm not sure whether I multiply the -12ln3 with the (3^-12x). Even if that is correct or not, I don't understand how to get the second derivative as I'm not sure on how to derive logs >.<

The second one would incorporate the chain rule?

Therefore for x^-2x:

let y= x^u , u = -2x

dy/dx = u(x) . -2 = 4x^2

And for - (e^2x)/5:

let y= - (e^u)/5 , u= 2x

dy/dx = (e^u)/5 . 2 = (2e^2x)/5

I'm not sure on how to handle the /5 and on how to derive the first derivative, especially when they deal with exponential and logs.

If you could further explain where I've gone wrong, I would be grateful.
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Re: first and second derivatives of these equations

Postby Martingale on Tue Aug 24, 2010 7:02 pm

Let me give you an example...

let

I want to find

first I take the log (natural log) of both sides



now take the derivative of both sides



then



now replace

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Postby stapel_eliz on Tue Aug 24, 2010 7:04 pm

doodoo21 wrote:I don't understand how to get the second derivative as I'm not sure on how to derive logs

Ouch! They were supposed to teach you that stuff before assigning homework on it! :shock:

To learn how to work with exponential and logarithmic functions and their derivatives, try here. :wink:

doodoo21 wrote:The second one would incorporate the chain rule?

You can not apply rules for constants to situations with variables. You have the Power Rule for differentiating xn where n is a number; you have the exponential derivative rule for differentiating nx where n is a number. You cannot use either of those rules for xf(x).

Have you learned about logarithmic differentiation yet?
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Re:

Postby doodoo21 on Wed Aug 25, 2010 1:51 pm

stapel_eliz wrote:Ouch! They were supposed to teach you that stuff before assigning homework on it! :shock:

To learn how to work with exponential and logarithmic functions and their derivatives, try here. :wink:


Thanks for helping. Im doing a master of finance course with no background knowledge on calculus. The lecturer/tutor expected us to know it all so he powered through it :S...Thats why I am in need of assistance!

I would like to know if dy/dx of the first equation is 2 - 12ln3(3^-12x)...I'm still unsure on how it's meant to come out.

stapel_eliz wrote:You can not apply rules for constants to situations with variables. You have the Power Rule for differentiating xn where n is a number; you have the exponential derivative rule for differentiating nx where n is a number. You cannot use either of those rules for xf(x).

Have you learned about logarithmic differentiation yet?


Thank you again...from my understanding dy/dx of the second equation would be: (x^-2x)[ln(x)-2] - (2e^2x)/5

Is this all correct? Thank you again guys.
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Postby stapel_eliz on Wed Aug 25, 2010 4:45 pm

doodoo21 wrote:I would like to know if dy/dx of the first equation is 2 - 12ln3(3^-12x).

Sorry, but no.

doodoo21 wrote:from my understanding dy/dx of the second equation would be: (x^-2x)[ln(x)-2] - (2e^2x)/5

You're close, but not quite right.

Please reply showing your steps, so we can try to find the errors. Or review here. :wink:
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