Question

give me example problems about:
deriving hyperbolic functions
(please post it below)

Answer 1

what is the value of \[\cosh^2 x-\sinh^2 x\]is a good example for workin on this concept

Answer 2

it is equivalent to 1...

Answer 3

i mean.....
give me like a quiz about deriving hyperbolic functions...:)

Answer 4

can u give me a simple one so i can give u similar one

Answer 5

try to find sinh(A+B) = ?
or is it too simple for you ?

Answer 6

like:
find y' of
y = cosh (sin x)

Answer 7

differentiate,
\(\huge \frac{cosh\quad lnx+sinh\quad lnx}{cosh\quad lnx-sinh\quad lnx}\)

Answer 8

wait

Answer 9

waiting......

Answer 10

not sure...
\[\frac{ [\cosh(lnx)-\sinh(lnx)][\frac{ \sinh(lnx) }{ x }+\frac{ \cosh(lnx) }{ x }]-[\cosh(lnx)+\sinh(lnx)][\frac{ \sinh(lnx) }{ x }-\frac{ \cosh(lnx) }{ x }]}{ [\cosh(lnx)-\sinh(lnx)]^2 }\]

Answer 11

lol,. the answer is 2x :P

Answer 12

don't differentiate as it is, first simplify as much as u can.

Answer 13

lol

Answer 14

simplify? how?

Answer 15

use cosh y as 1/2(e^y+e^-y)
then use log property

Answer 16

thanks!!
more samples please?

Answer 17

but could u do it ??

Answer 18

f(x)= \[\frac{ e ^{lnx} }{ e ^{-lnx} }\]
is that right?

Answer 19

yup, what is e^{ln x} = ??

Answer 20

?
instead of x or y
i used ln x <----given
confused...
what is your complete solution?

Answer 21

e^{ln x} = x
e^-{ln x} =1/ x

x/(1/x) = x^2
d/dx(x^2) = 2x
as simple as it is.

Answer 22

next problem, differentiate tanh^-1 (sin x)

Answer 23

or prove d/dx(tanh^-1 (sin x))=sec x

Answer 24

we haven't study about inverse of hyperbolic func..

Answer 25

integration ?

Answer 26

just pre-cal...not yet on integration

Answer 27

differentiate cosh^3 2x

Answer 28

and then sinh (e^x)

Answer 29

y'= 6 cosh^2 (2x) sinh (2x)
y' =e^(x) [cosh (e^x)]
correct?

Answer 30

yup.
diff. sqrt(coth 4x)

Answer 31

y'=-4csch^2(4x)

Answer 32

?
no
it was \(\sqrt{coth4x}\)

Answer 33

lol..sorry
y'=\[\frac{ -4csch^2(4x) }{ 2\sqrt{\coth(4x)} }\]
?

Answer 34

yup. thats correct.
next : differentiate cosh 5x sinh 3x

Answer 35

\[y'= 5[\sinh(5x)\sinh(3x)]+3[\cosh(5x)\cosh(3x)]\]
?

Answer 36

yup, now make one question for yourself and solve it.

Answer 37

thanks a lot!! :))

Answer 38

welcome :)