Differentiate f(x)=Coshx/Sinh(x2)
can anybody give me the solution to this?
Thank you...

Question

Differentiate f(x)=Coshx/Sinh(x2)
can anybody give me the solution to this? 
Thank you...

anonymous · Answer

thats is x square.....

terenzreignz · Answer

Well, basics... quotient rule, first.

terenzreignz · Answer

$$\large \frac{d}{dx}\frac{f(x)}{g(x)}=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}$$

terenzreignz · Answer

In this case
f(x)=cosh x
g(x)= sinh x²

anonymous · Answer

yes I did that... but the answer am getting is not correct... I think it requires trigonometric substitutions...

terenzreignz · Answer

Could you post your solution?

anonymous · Answer

Yes one minute...

anonymous · Answer

$$Sinhx ^{2} .Sinhx+ Coshx. 2x Coshx ^{2} / (Sinhx ^{2})^{2}$$

terenzreignz · Answer

I for one, don't see what's wrong with it...

anonymous · Answer

how to further simplify that?

terenzreignz · Answer

None that I know of... Hyperbolic functions confuse me somewhat... unless you're suggesting we expand the sinh and cosh into the forms involving powers of e.

anonymous · Answer

ohh then I guess this is the final answer.....

sirm3d · Answer

shouldn't it be ( ) ( ) MINUS ( ) ( )

terenzreignz · Answer

!!!!!!!!
Completely overlooked that.
Bloody details -.-

It should indeed be
sinh x² sinh x + 2x cosh x cosh x²
in the numerator

anonymous · Answer

no no it is PLUS...

terenzreignz · Answer

My bad.

terenzreignz · Answer

It's not plus...
unlike the trigonometric cos
the derivative of 
cosh x
is
sinh x

terenzreignz · Answer

^as opposed to the derivative of
cos x
being
-sin x

anonymous · Answer

well,  it is my fist day here, did not expect people would respond, am amazed and very happy I found this site... thank you :) :) @terenzreignz @sirm3d ..... I guess it cannot be simplified any further in trig terms... thank you :)

terenzreignz · Answer

No problem :)

sirm3d · Answer

you're welcome.