I need help with the following derivatives

y= (e^1/x) / x^2

f(t) = t ln(5t)

thanks for your help

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- April 13th 2010, 07:05 PMtim_manniredifferentiation
I need help with the following derivatives

y= (e^1/x) / x^2

f(t) = t ln(5t)

thanks for your help - April 13th 2010, 07:17 PMdrumist
Could you show us what exactly is giving you trouble? What do you get when you attempt them?

- April 13th 2010, 07:18 PMharish21
- April 14th 2010, 03:45 AMtim_mannire
Using the rules you suggested i got

dy/dx = ((x^2)(e^1/x) - (e^1/x)(2x)) / x^4

f ' (t) = (1/5t) (t)

are they correct? - April 14th 2010, 04:50 AMe^(i*pi)
- April 14th 2010, 06:25 AMtim_mannire
thanks for your help. I have tried what you suggested but I just don't understand (Headbang). A complete working of the question using the rules would help me to understand.

thank you - April 14th 2010, 06:38 AMe^(i*pi)

For this we need to use the quotient rule which is:

In your case and

I will differentiate the numerator as that's what seems to be the issue then you can try using my value of in the quotient rule. FYI my final answer is

To find u' (du/dx) we need to work out .

For simplicity and clarity's sake let . From the chain rule we know that

Due to this substitution we can rewrite u as .

Differentiating this function is easy:

Similarly 1/x is also easy to differentiate:

From the chain rule above:

Since we get in terms of x:

Therefore - April 14th 2010, 09:43 AMdrumist