Simple differentiation for YOU PPL

[beanryu]

how do I differentiate 4*x^(2x)?
The professor explained to the class while i was sleeping...
and I don't quite get what my fd was talking about...

can anyone help?
I know x^(2x) is different from a constant to (2x)
but I don't no how to do it...

is the answer (x^x)(lnx)+(x^x)
if so could you guys explain it step by step? THANX!

 

[Pseudo Statistic]

Call it a function, y:
y = 4x^(2x)
There's one easy way to do it that I can think of...
First thing we do, let's ignore the 4... it'll probably end up confusing you; what we'll do with the final answer is multiply it before, so let's define a new function z:
z = x^(2x)
Apply log to both sides...
log z = 2x log x
Use the chain and product rule..
z'/z = 2log x + 2
z' = (x^2x)(2log x + 2)
Now, times the whole thing by 4...
y' = (4x^2x)(2log x + 2)

By the way I think this should be in the homework help forum or the calculus forum..

 

[beanryu]

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