Find f'(x^(2tan(x))… - QuestionCove
OpenStudy (anonymous):

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

3 years ago
OpenStudy (turingtest):

could you show what you have so far?

3 years ago
OpenStudy (anonymous):

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)))

3 years ago
OpenStudy (turingtest):

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

3 years ago
OpenStudy (anonymous):

yeah i couldn't write that in the quesiton

3 years ago
OpenStudy (turingtest):

why did you plug in pi/2 ?

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

3 years ago
OpenStudy (turingtest):

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

3 years ago
OpenStudy (turingtest):

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

3 years ago
OpenStudy (anonymous):

yessum

3 years ago
OpenStudy (turingtest):

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

3 years ago
OpenStudy (turingtest):

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

3 years ago
OpenStudy (anonymous):

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

3 years ago
OpenStudy (anonymous):

To me, your derivative is not correct

3 years ago
OpenStudy (turingtest):

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

3 years ago
OpenStudy (turingtest):

$2(x)^{2\tan x})[(\tan x)/(x)+\ln(x)/(\cos^2(x))]$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?

3 years ago
OpenStudy (anonymous):

sorry if i was unclear.

3 years ago
OpenStudy (turingtest):

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

3 years ago
OpenStudy (turingtest):

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

3 years ago
OpenStudy (turingtest):

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

3 years ago
OpenStudy (anonymous):

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!

3 years ago
OpenStudy (turingtest):

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

3 years ago
OpenStudy (anonymous):

it sure did i really appreciate the explanation

3 years ago
OpenStudy (turingtest):

happy to help!

3 years ago