An identitiy for hyperbolic functions
up vote
2
down vote
favorite
Let $y$ be a paramater and $f(x)=frac{sinh(xy)}{xsinh y}$. The question is $f^{prime}(3)=?$ I find the answer as $$f^{prime}(3)=frac{3ycosh(3y)-sinh(3y)}{9sinh y}.$$
But the answer of book is $$f^{prime}(3)=coth (3y)- frac{1}{3 y}.$$
I can not see the identity (if it is true)
$$frac{3ycosh(3y)-sinh(3y)}{9sinh y}=coth (3y)- frac{1}{3 y}.$$
calculus algebra-precalculus
asked Nov 26 at 12:48
user315531
13513
add a comment |
up vote
2
down vote
favorite
Let $y$ be a paramater and $f(x)=frac{sinh(xy)}{xsinh y}$. The question is $f^{prime}(3)=?$ I find the answer as $$f^{prime}(3)=frac{3ycosh(3y)-sinh(3y)}{9sinh y}.$$
But the answer of book is $$f^{prime}(3)=coth (3y)- frac{1}{3 y}.$$
I can not see the identity (if it is true)
$$frac{3ycosh(3y)-sinh(3y)}{9sinh y}=coth (3y)- frac{1}{3 y}.$$
calculus algebra-precalculus
asked Nov 26 at 12:48
user315531
13513
1
It isn't true. Set $y=1$ and compare the values. Not even close.
– saulspatz
Nov 26 at 13:29
There is probably a typo - in your solution or in the book. Simple exchange $y$ to $x$ (or vice versa) in one denominator makes them equal.
– user376343
Nov 27 at 8:48
1
I do not really believe that both answers are correct. It looks like that you've evaluated first derivative but not the third. And the answer in your book seems to be too "simple" for the value of the third derivative
– Mikalai Parshutsich
Nov 27 at 11:27
@MikalaiParshutsichYou are right. I had made a typo. I edit the question.
– user315531
yesterday
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Let $y$ be a paramater and $f(x)=frac{sinh(xy)}{xsinh y}$. The question is $f^{prime}(3)=?$ I find the answer as $$f^{prime}(3)=frac{3ycosh(3y)-sinh(3y)}{9sinh y}.$$
But the answer of book is $$f^{prime}(3)=coth (3y)- frac{1}{3 y}.$$
I can not see the identity (if it is true)
$$frac{3ycosh(3y)-sinh(3y)}{9sinh y}=coth (3y)- frac{1}{3 y}.$$
calculus algebra-precalculus
asked Nov 26 at 12:48
user315531
13513
Let $y$ be a paramater and $f(x)=frac{sinh(xy)}{xsinh y}$. The question is $f^{prime}(3)=?$ I find the answer as $$f^{prime}(3)=frac{3ycosh(3y)-sinh(3y)}{9sinh y}.$$
But the answer of book is $$f^{prime}(3)=coth (3y)- frac{1}{3 y}.$$
I can not see the identity (if it is true)
$$frac{3ycosh(3y)-sinh(3y)}{9sinh y}=coth (3y)- frac{1}{3 y}.$$
calculus algebra-precalculus
calculus algebra-precalculus
asked Nov 26 at 12:48
user315531
13513
asked Nov 26 at 12:48
user315531
13513
edited yesterday
asked Nov 26 at 12:48
user315531
13513
asked Nov 26 at 12:48
user315531
13513
asked Nov 26 at 12:48
user315531
13513
13513
1
It isn't true. Set $y=1$ and compare the values. Not even close.
– saulspatz
Nov 26 at 13:29
There is probably a typo - in your solution or in the book. Simple exchange $y$ to $x$ (or vice versa) in one denominator makes them equal.
– user376343
Nov 27 at 8:48
1
I do not really believe that both answers are correct. It looks like that you've evaluated first derivative but not the third. And the answer in your book seems to be too "simple" for the value of the third derivative
– Mikalai Parshutsich
Nov 27 at 11:27
@MikalaiParshutsichYou are right. I had made a typo. I edit the question.
– user315531
yesterday
add a comment |
1
It isn't true. Set $y=1$ and compare the values. Not even close.
– saulspatz
Nov 26 at 13:29
There is probably a typo - in your solution or in the book. Simple exchange $y$ to $x$ (or vice versa) in one denominator makes them equal.
– user376343
Nov 27 at 8:48
1
I do not really believe that both answers are correct. It looks like that you've evaluated first derivative but not the third. And the answer in your book seems to be too "simple" for the value of the third derivative
– Mikalai Parshutsich
Nov 27 at 11:27
@MikalaiParshutsichYou are right. I had made a typo. I edit the question.
– user315531
yesterday
1
1
It isn't true. Set $y=1$ and compare the values. Not even close.
– saulspatz
Nov 26 at 13:29
It isn't true. Set $y=1$ and compare the values. Not even close.
– saulspatz
Nov 26 at 13:29
There is probably a typo - in your solution or in the book. Simple exchange $y$ to $x$ (or vice versa) in one denominator makes them equal.
– user376343
Nov 27 at 8:48
There is probably a typo - in your solution or in the book. Simple exchange $y$ to $x$ (or vice versa) in one denominator makes them equal.
– user376343
Nov 27 at 8:48
1
1
I do not really believe that both answers are correct. It looks like that you've evaluated first derivative but not the third. And the answer in your book seems to be too "simple" for the value of the third derivative
– Mikalai Parshutsich
Nov 27 at 11:27
I do not really believe that both answers are correct. It looks like that you've evaluated first derivative but not the third. And the answer in your book seems to be too "simple" for the value of the third derivative
– Mikalai Parshutsich
Nov 27 at 11:27
@MikalaiParshutsichYou are right. I had made a typo. I edit the question.
– user315531
yesterday
@MikalaiParshutsichYou are right. I had made a typo. I edit the question.
– user315531
yesterday
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3014282%2fan-identitiy-for-hyperbolic-functions%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
It isn't true. Set $y=1$ and compare the values. Not even close.
– saulspatz
Nov 26 at 13:29
There is probably a typo - in your solution or in the book. Simple exchange $y$ to $x$ (or vice versa) in one denominator makes them equal.
– user376343
Nov 27 at 8:48
1
I do not really believe that both answers are correct. It looks like that you've evaluated first derivative but not the third. And the answer in your book seems to be too "simple" for the value of the third derivative
– Mikalai Parshutsich
Nov 27 at 11:27
@MikalaiParshutsichYou are right. I had made a typo. I edit the question.
– user315531
yesterday