Hi all. Help with logarithmic differentiation please.
Use logarithmic differentiation to find
d/dx x^(2cos(x))
+129845 y = x^(2cosx)
lny = lnx^(2cosx)
lny = 2cosx* [ln x] [ use the product rule to differentiate the right side ]
y' / y = -2sinx*lnx - 2cosx[ 1/x]
y' / y = [-2*x*sinx*lnx - 2cosx] / x multiply both sides by y [ and y = x^(2cosx)]
y ' = x^(2cosx) * [ -2*x*sinx*lnx - 2cosx] * [x^(-1)]
y ' = -2 * [ x^(2cosx)* x^(-1) ] [ x*lnx*sinx - cosx]
y ' = -2 * [ x^(2cosx - 1) ] * [x*nx*sinx - cosx]
