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Calculus/A Calculus Question under differentiation

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Expert: - 2/10/2008


Question

The Question
"Please, i'm having problems with a particular question under calculus.
Here it is

y=e^2x^2^2x^2 x logex

Pls i'm sure of this question. Check attached image. i will really like
a reply as soon as possible. Thanks"


Answer
The problem starts with a product rule.  d(a(x)b(x)) = a'b + b'a.  
b'a is a/x.  a'b, however, is a bit longer.  It involves a lot of chain rules.  We have s=(something 1)^2, so the derivative is 2s^2-1 ds.  s is t=(something 2) to the 2x, so the derivative is t^(2x-1)dt.  Ans so on and so forth.

This keeps going and eventually the last thing to take the derivatve of is e^(2x), which is 2e^(2x).

So this problem would appear to be a long chain rule with a lot of work, but none is complicated and each derivative along the way is known.  The answer, though fairly straightforward, turns out to be quite long.  Make sure everything is copied correctly!

Scotto

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