Hi

I need help on the following questions:

1)Prove that:

This is what i have done:

stuck at this part

2) Find the derivative of

This is what i have done:

3) Find the derivative of

What have i done wrong??

P.S

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- Apr 22nd 2010, 05:04 AMPaymemoneyA Few Differentiation Questions
Hi

I need help on the following questions:

1)Prove that:

This is what i have done:

stuck at this part

2) Find the derivative of

This is what i have done:

3) Find the derivative of

What have i done wrong??

P.S - Apr 22nd 2010, 05:40 AMcraig
For the first 1.

Differentiating wrt :

Since , - Apr 22nd 2010, 03:06 PMPaymemoney
- Apr 22nd 2010, 03:15 PMPaymemoney
don't worry i know now, its from the identity

- Apr 22nd 2010, 05:53 PMPaymemoney
can anyone answer my other question?

- Apr 22nd 2010, 06:38 PMDiemo
3) Find the derivative of [tex]e^{-2x}sinh{5x}

Use the cain rule. Lut u = , and v = sinh(5x). Then

That give the right answer? - Apr 23rd 2010, 12:19 AMPaymemoney
yep thats correct, thanks

- Apr 23rd 2010, 12:24 AMPaymemoney
can anyone help me on question 2)

I have tried it again and i still get the same answer - Apr 23rd 2010, 06:25 AMDiemo
The reason you get the same answer on question two is because it is the right answer. According to wolframalpha anyhow.

Possibly it is in the form

, where all I have done there is takke the 3 inside of the square root and simplify. - Apr 23rd 2010, 03:18 PMPaymemoney
- Apr 24th 2010, 08:08 AMDiemo
Why would you simplify? There are a few reasons. Mainly if you are using it in some future equation though. It makes it much much easier to write, so if you are actually using the result in a larger equation it makes it easier to keep track of things.

Secondly, while it doesn't matter in your case, consider the derivative of . YOu can of course rewrite it in it's current form to be and use something like the product rule or the chain rule to solve, which would be long and complicated. Or you could note that is just 1, hence the derivative is zero. and so on and so forth.

It is a good habit to get into to simplify as much as possible before doing the work. As Skeeter says, work smart not hard, which is something that applied mathematicians (like me) believe in. I once had a lecturer who found out that the place that we had our class was the other side of campus (maybe a ten minute walk) and was too lazy to walk out that far (possibly had other classes to be fair), so he moved the room, and we spent the entire semester squashed up in a room that was waaay to small to hold the entire class. Be lazy about things.