Question

find the partial derivatives
fx (pi/3,1) if f(x,y)=x ln (y cos x)

Answer 1

consider y as a constant and differentiate wrt x,
$$f_x(x,y)=\ln(y\cos x)+x\frac{-y\sin x}{y\cos x}=\ln(y\cos x)-x\tan x$$
now substitute x,y with pi/3 and 1 respectively
$$f_x(\pi/3,1)=\ln(1.\cos(\pi/3))-\frac \pi3\tan\frac \pi 3=-\ln2-\frac \pi{\sqrt{3}}$$