logarithmic differentiation
posted by Ashley .
How do you find the logarithmic differentiation of y = x^cos x ?

first take ln of both sides
ln y = ln(x^cosx)
ln y = cosx lnx
now differentiate with respect to x
(dy/dx)/y = cosx (1/x) + lnx (sinx)
dy/dx = y ( (1/x)cosx + lnx(sinx))
= x^cosx ( (1/x)cosx + lnx(sinx))