dervative help

mark

New member
Joined
Feb 28, 2006
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43
im having trouble with this problem and i dont know if my work is right

obtain dy/dx

e^y+e^x = sinhy

heres my work

e^y + e^x = sinhy

ln (e^y) + ln (e^x) = ln( sinhy)

y + x = ln(sinhy)

dy/dx + 1 = cothy dy/dx

from here i do not know what to do
 
Why not do this?
\(\displaystyle \L
\begin{array}{l}
e^y y' + e^x = \cosh (y)y' \\
y' = \frac{{ - e^x }}{{e^y - \cosh (y)}} \\
\end{array}\)
 
Hello, mark!

im having trouble with this problem   \displaystyle \; . . . I'm not surprised!

Obtain dydx:    ey+ex=sinhy\displaystyle \frac{dy}{dx}:\;\;e^y\,+\,e^x \:=\:\sinh y

heres my work

ey+ex  =  sinhy\displaystyle e^y\,+\,e^x\;=\;\sinh y

ln(ey)+ln(ex)  =  ln(sinhy)    \displaystyle \ln(e^y)\,+\,\ln(e^x)\;=\;\ln(\sinh y)\;\; . . . what?

y+x  =  ln(sinhy)    \displaystyle y\,+\,x\;=\;\ln(\sinh y)\;\; . . . WHAT?

dydx+1  =  cothy(dydx)    \displaystyle \frac{dy}{dx}\,+\,1\;=\;\coth y\left(\frac{dy}{dx}\right)\;\;

from here i do not know what to do     \displaystyle \;\;Yes, you do . . . solve for dy/dx . . .
We have: \(\displaystyle \L\,e^y\,+\,e^x\;=\;\sin y\)

Differentiate implicitly: \(\displaystyle \L\,e^y\left(\frac{dy}{dx}\right)\,+\,e^x\;=\;\cosh y\left(\frac{dy}{dx}\right)\)


Okay, one more time . . .

How do we solve for dydx\displaystyle \frac{dy}{dx} ?

We get all the dydx\displaystyle \frac{dy}{dx} terms on one side . . .

\(\displaystyle \L\,e^y\left(\frac{dy}{dx}\right)\,-\,\cosh y\left(\frac{dy}{dx}\right)\;=\;-e^x\)

Factor: \(\displaystyle \L\:\left(e^y\,-\,\cosh y\right)\left(\frac{dy}{dx}\right)\;=\;-e^x\)

Therefore: \(\displaystyle \L\:\frac{dy}{dx}\;=\;\frac{-e^x}{e^y\,-\,\cosh y}\;\;\) . . . or: \(\displaystyle \L\,\frac{e^x}{\cosh y\,-\,e^y}\)
 
WHY E ^ X IS ITSELF AND NOT DY/DX IN FRONT OF IT? IS THAT BECAUSE YOU FIND Y INSTEAD OF X AND THEREFORE; YOU DO NOT GET DY/DX FOR E^X? What happen if you have two xy terms with like x^2y something like that with one with a power of 2 and one without?
 
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