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How to differentiate x^(cosx) = y^(sinx) with respect to x

by styxrihocc
Tags: differentiate, respect, xcosx, ysinx
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styxrihocc
#1
Apr18-12, 12:34 PM
P: 10
1. The problem statement, all variables and given/known data

Differentiate x^(cosx) = y ^(sinx) with respect to x

2. Relevant equations



3. The attempt at a solution
I tried using natural logs but im not sure if its correct, if it's wrong please point me to the right direction, thanks

x^(cosx) = y^(sinx)
ln x^(cosx) = ln y ^(sinx)
ln x (cosx) = ln y (sinx)
cosx/x - sinx lnx = cosx lny +sinx/y (dy/dx)
cosx/x - sinx lnx - cosx lny = sinx/y (dy/dx)
(cosx/x - sinx lnx - cosx lny) / (sinx/y) = dy/dx
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LCKurtz
#2
Apr18-12, 01:06 PM
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Quote Quote by styxrihocc View Post
1. The problem statement, all variables and given/known data

Differentiate x^(cosx) = y ^(sinx) with respect to x

2. Relevant equations



3. The attempt at a solution
I tried using natural logs but im not sure if its correct, if it's wrong please point me to the right direction, thanks

x^(cosx) = y^(sinx)
ln x^(cosx) = ln y ^(sinx)
ln x (cosx) = ln y (sinx)
cosx/x - sinx lnx = cosx lny +sinx/y (dy/dx)
cosx/x - sinx lnx - cosx lny = sinx/y (dy/dx)
(cosx/x - sinx lnx - cosx lny) / (sinx/y) = dy/dx
Your work is correct. You could be slightly less ambiguous with parentheses though.
styxrihocc
#3
Apr18-12, 01:17 PM
P: 10
Thanks.


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