Anyone good at Calculus, specifically Derivatives?

[Miss Kelly]

If so, PLEASE help me find the derivative of:

1) X ^ e

And Simplify:

2) (e^5x/2-e^3x)/(square root of e^2)


I have worked on these for a week and still cannot figure out the answer. If you can just get me started, that would be great!

Thank you!

Kelly

 

[Saffron]

Not me!

 

[Meriweather]

Not me either....but I have a couple of math whizzes that live here........but they aren't home right now.

If you don't receive your help by then, I will get them on it

 

[Disney845]

ummm ok....it has been awhile since calc. classes for me...but I will try.


1. X^e


e X ^ (-1+e)


edit: I was going to type in an explaination, but it ended up looking slightly confusing what with the way you have to type mathematical terms on the comp. sorry I couldn't do a better job with an explaination!!

 

[damo]

It's hard to print on the computer but here goes:

y=x^e

since e is just a number the derivative is
dy/dx=e[x^(e-1)]

just like if y=x^3 then dy/dx is 3x^2

For the second question is the question
[(e^5x)/(2-e^3x)]/root e^2 ?? not sure where the brackets all go

The root of e^2 is just e so that part is simple but I can't understand if the e^(5x) is all divided by 2-[e^(3x)] or what. Try to rewrite it putting all the brackets in.

 

[Miss Kelly]

Damo: Yes, where you have the brackets is correct.

Thanks for the responses everyone. I didn't even know where to start.

Thanks again.

 

[damo]

so it is e to the 5x all divided by 2 - (e to the 3x) and all of that is divided by root of e squared?

[e^(5x)] / [2 - (e^(3x)] / root(e^2)

that doesn't seem like much of a question

you would get
[e^(5x)][e] / [2 - [e^(3x)]]

which simplifies to
[e^(5x+1)] / [2-(e^(3x))]

 

[Miss Kelly]

Oh no, wait, its [e^5x/2-e^3x] / [sq root of (e^2)]

Is that any better? The 5x/2 is a fraction. I don't why they just didn't put 5/2x.

Also,

If you differeniate e^(sq root of e) is it 1/2e^-1/2e? I used the power rule, I believe.

Thanks again damo. I really appreciate the help.

Kelly

 

[Zurg]

Ouch.

 

[damo]

e^(sqrt(e)) is just a number so the derivative would be zero, just like the derivative of 2 is zero. Are you sure there isn't an x in there somewhere?

Now for the second one, if the question is
[e^(5x/2) - e^(3x)] / sqrt(e^2)

then question simplifies to
[e^(5x/2) - e^(3x)] / e

= e^[(5x-2)/2] - e^(3x-1)

Is that how far they want you to simplify or do they want you to take out a common factor yet? How far have you had to simplify your other questions?

 

[DonnaS]

I liked math until I took calculus. LOL

 

[Meriweather]

Here is the answer I got from DH

1) X ^ e


e*(X^(e-1) ) e is just a number, d(x^a)/dt = a*(x^(a-1))


And Simplify:

2) (e^5x/2-e^3x)/(square root of e^2)


-(e^(5x-1))/((e^3x) -2)

 

[damo]

Meriwether in #2 the first exponent is 5x/2, the 2 goes with the first term not in the denominator. The question is hard to read on the internet.

 

[Miss Kelly]

Damo: Definately no x in the e^(sqrt(e)) . Thanks again for all of your help.

DonnaS: Yeah, me too. LOL!

Meriweather: Thanks a bunch. Tell your hubby I said Thanks too!




Done(for now)!!!

 

[damo]

Anytime, glad to help