Posted by ken on Saturday, March 2, 2013 at 10:53pm.
sorry for the probably simple question, but i haven't done this stuff in a long, long time.
thought i had this right, but again not finding the answer
which of the following gives the slope of the tangent line to the graph of y=2^(1x) at x=2?
a)1/2
b)1/2
c)2
d)2
e)(ln2)/2
so... it thought y=2^1x)
then y'=(1x)(2^(1x1))
at x=2
then y'=(12)(2^(121))
y'= 1(2^(2))
y'= 1/4
any help figuring out where i went wrong would be greatly appreciated.
thank you

calculus  Reiny, Saturday, March 2, 2013 at 11:51pm
y = 2^(1x) is an exponential function, which is differentiated using natural logarithms
dy/dx = 2^(1x) (1) ( ln2)
so when x = 2,
dy/dx = ln2(2^(12)
= ln2 (1/2) = (1/2)ln2 , looks like e
as soon as I had my derivative which contained ln2, I knew that the first 4 choices were not correct.
You found the derivative as if it was a polynomial function where the terms are such that the base is the variable, such as 3x^5
e.g.
compare 4^x with x^4
if y = x^4
dy/dx = 4x^3
but
if y = 4^x
dy/dx = ln4 (4^x)

calculus  ken, Sunday, March 3, 2013 at 12:37am
Thanks Reiny,really appreciate the extra explanation. get it now. thank you
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