Question

differentiate y=cosec^-1(x^2-1)

Answer 1

csc derives similar to sec;

sec' = sec tan

csc' = -csc cot

Answer 2

but this is inverse stuff ....

Answer 3

csc-1(x)=y

x = csc(y) ; derive

1 = -csc(y) cot(y) y' ; solve for y'



1
----------- = y'
-csc(y) cot(y)

the rest is just reforming those y parts back into xs

Answer 4

since csc(y) = x thats an easy one

1
------- = y'
-x cot(y)

for the cot, it might be good to build a righty:

cot(y) = sqrt(x^2-1)


1
- ------------- = y'
x sqrt(x^2-1)

Answer 5

of course, you want to implement your argument into this :)

Answer 6

i shoulda used a more generic "u" rather than an "x" prolly.

lets say: u = x^2-1, then


u'
- ------------- = y'
u sqrt(u^2-1)

and so we simply rewrite the us back into (x^2-1)s

Answer 7

\[-2/{(x ^{2}-1)\sqrt{(x ^{2}-2})}\] i was looking for an answer to this prob and this is what i got. want to know whether this is correct or not.

Answer 8

the -2 is good

the x^2-1 is good

as long as: sqrt((x^2-1)^2 -1) pans out ....

Answer 9

(x^2-1)^2 = x^4 -2x^2 +1

x^4 -2x^2 +1 - 1 = x^4 -2x^2

x^4 -2x^2 = x^2 (x^2-2)

sqrt(x^2 (x^2-2)) = x sqrt(x^2-2)

Answer 10

id say your missing an "x"

Answer 11

derivative of (x^2-1) at the end gives 2x and x is cancelled.

Answer 12

yay!! ... then your right ;)

Answer 13

i good place to remove the human element when checking answers is:

wolframalpha.com