How to differentiate x^(cosx) = y^(sinx) with respect to xby styxrihocc Tags: differentiate, respect, xcosx, ysinx 

#1
Apr1812, 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 



#2
Apr1812, 01:06 PM

HW Helper
Thanks
PF Gold
P: 7,187





#3
Apr1812, 01:17 PM

P: 10

Thanks.



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