anonymous
  • anonymous
when u are having in this form then how to differentiate :) tan^-1(2^(x+1)/(1-4^x)) can i use substitution here ?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
i don't think so substitution will work
hartnn
  • hartnn
substitute 2^x = tan y
hartnn
  • hartnn
lol, why not ?

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hartnn
  • hartnn
do you know tan 2 theta formula ?
anonymous
  • anonymous
coz i have never did this type of question lol
anonymous
  • anonymous
yep :)
anonymous
  • anonymous
2tanα/(1 – tan²α)
hartnn
  • hartnn
2^(x+1) = 2. 2^x , 4^x = (2^x)^2 plug in 2^x = tan y and see the magic! (simplification :P)
anonymous
  • anonymous
will it really works :PPPP lol i hate chain rule -_-
anonymous
  • anonymous
don't wanna use chain rule for inverse trig ...........
hartnn
  • hartnn
? what did you get after simplification ?
hartnn
  • hartnn
i don't think chain rule is required here...
anonymous
  • anonymous
wait :))
anonymous
  • anonymous
use tan(x+y)=(tanx+tany)/(1-tanxtany)
anonymous
  • anonymous
@Abhishek619 :/
hartnn
  • hartnn
same thing....tan 2 thetha comes from tan (x+y) formula only
anonymous
  • anonymous
|dw:1372850429715:dw|
anonymous
  • anonymous
oh :O
anonymous
  • anonymous
@Abhishek619 -oh :OO yeah we can do it in that way also :OOO tahnx :)
hartnn
  • hartnn
with substitution, you would have got the same thing...
anonymous
  • anonymous
let me first @hartnn use ur method :D
anonymous
  • anonymous
@Abhishek619 @hartnn -answer is [2^(x+1)loge2]/(1+4^x) :'(
hartnn
  • hartnn
i am never interested in final answer, just the method..... if your algebra part is correct, you WILL get correct final answer....
anonymous
  • anonymous
but the answer is in loge2 and having (1+4^x) also
anonymous
  • anonymous
well did he wrote 2tan^-12^x?????????
anonymous
  • anonymous
2tan^-1(2^x)
hartnn
  • hartnn
ok, got till 2 tan inverse 2^x, right ? if you diff. that u get 2 * (1/1+(2^x)^2) 2^x ln 2 (ln = log_e) .... (2^x ln 2 comes from chain rule) yes...
anonymous
  • anonymous
oh x is in power :O
anonymous
  • anonymous
then m getting the answer :)
hartnn
  • hartnn
yeah... (2^x)^2 = 4^x and 2.2^x = 2^(x+1) good!
anonymous
  • anonymous
@hartnn -thanx :) now i can do the rest ^_^
hartnn
  • hartnn
welcome ^_^

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