SOLUTION: Hello everyone, finding the following question puzzling, i have not covered this before, and am trying to get a heads up for when i start my course Use logarithmic differentiati

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hello everyone, finding the following question puzzling, i have not covered this before, and am trying to get a heads up for when i start my course Use logarithmic differentiati      Log On


   

Question 375065: Hello everyone, finding the following question puzzling, i have not covered this before, and am trying to get a heads up for when i start my course
Use logarithmic differentiation to differentiate the following:
(i) y = 2^x (ii) y = x^x
Cheers
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
i)

y=2%5Ex Start with the given equation.


ln%28y%29=ln%282%5Ex%29 Take the natural log of both sides.


ln%28y%29=x%2Aln%282%29 Pull down the exponent.


... Derive both sides


... Solve for y'


... Now plug in y=2%5Ex


Note: the derivative of b%5Ex is b%5Ex%2Aln%28b%29

-----------------------------------------------

ii)

y=x%5Ex Start with the given equation.


ln%28y%29=ln%28x%5Ex%29 Take the natural log of both sides.


ln%28y%29=x%2Aln%28x%29 Pull down the exponent.


... Derive both sides


... Solve for y'


... Now plug in y=x%5Ex

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You get one question per post. Since the first one is trivial, I'll do the second.



Take the natural log of both sides:





Differentiate both sides with respect to using the Chain Rule on the left and the Product Rule on the right:

Let .

Then

Hence:



Multiply both sides by





John

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