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d(2)-d(6z)

d(2) is 0, right?

yes

-6 is the answer

No its not. The answer is -6(1-6z) ln(2).

But I have no idea why there is a natural log.

http://www.wolframalpha.com/input/?i=%20Differentiate%20%20H(z)%20%3D%202%5E1-6z&t=crmtb01

i am right according to wolfram alpha ...see steps

Maybe I should have typed H(z) = 2^(1-6z)

check that what is the correct ans.

http://www.wolframalpha.com/input/?i=differentiate+H%28z%29+%3D+2%5E%281-6z%29

this was my fault for not writing the problem correctly

ok ... so u got the correct answer ?

Yes.