- #1
styxrihocc
- 10
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Homework Statement
Differentiate x^(cosx) = y ^(sinx) with respect to x
Homework Equations
The Attempt at a Solution
I tried using natural logs but I am 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