Question

Find f'(x^(2tan(x))), for x E (0,pi/2)

Answer 1

could you show what you have so far?

Answer 2

i took the derivative and plugged in pi/2

2(pi/2)^(2tan(pi/2))((tan(pi/2))/(pi/2)+ln(pi/2)/(cos^2(pi/2)))

Answer 3

I don't know what you mean by
x E (0, pi/2)
is it\[x\in\{0,\frac{\pi}2\}\]?

Answer 4

yeah i couldn't write that in the quesiton

Answer 5

why did you plug in pi/2 ?

Answer 6

i was told myininaya to flow the same steps. what should i do?

Answer 7

same steps as this http://openstudy.com/study#/updates/53bddee5e4b09e08a1c60d04

Answer 8

ah yes, ok let me do the actual differntiation and see what i get

Answer 9

yep, but that is f'(pi/2), and your question is for the interval (0,pi/2), right?

Answer 10

yessum

Answer 11

well in that case, we won't be plugging in the value, since we aren't evaluating the function at a point, but rather coming up with a formula for the function in that interval, so at least leave it in terms of x

Answer 12

the question is, what is the difference between the value of the derivative over that interval that makes it different from, say, (pi/2,pi)
usually in these problems one can assume that the limiting interval is to make the problem simpler, so I imagine your answer with x in place of pi/2 should be correct, but it would be nice to understand why they ask for that specific interval

Answer 13

so you are saying to plug in pi/2 then replace it with x?

the problem that i found is that the result of

2(pi/2)^(2tan(pi/2))((tan(pi/2))/(pi/2)+ln(pi/2)/(cos^2(pi/2)))

is indeterminate

Answer 14

To me, your derivative is not correct

Answer 15

maybe i am reading it wrong, it is difficult for me to see it without the LaTeX

Answer 16

\[2(x)^{2\tan x})[(\tan x)/(x)+\ln(x)/(\cos^2(x))]\]is what i got as the derivativeof\[f(x)=x^{2\tan x}\]
however that's not quite the same as asking what\[f'(x^{2\tan x})\]is, so are you sure you have the problem written correctly?

Answer 17

sorry if i was unclear.

Answer 18

oh, it's the dx on the bottom that makes all the difference here, otherwise we would have to know what f was

Answer 19

so what they want is the derivative written as a function over that interval, not evaluation at a point
so don't put int the pi/2 and replace it with x, simply never put the pi/2 at all
it only limits the answer

Answer 20

I see why they give you that interval now: because as you said, at pi/2 the derivative is undefined, hence limiting your answer to only concern the interval (0,pi/2) makes the problem simpler in that we don't need to consider the undefined point at pi/2, which makes the derivative discontinuous there

Answer 21

i see. so i submitted the 2(pi/2)^(2tan(pi/2))((tan(pi/2))/(pi/2)+ln(pi/2)/(cos^2(pi/2)))

since you said to replace the pi/2 with x. I got the problem correct I just wasn't quite sure what they were asking and the fact that i was discontinous at pi/2 had me confused. Not anymore!

Answer 22

I hope my explanation made sense, good luck on the next ones, if there are any :)

Answer 23

it sure did i really appreciate the explanation

Answer 24

happy to help!