Math Question. with solution. Thanks?

Sol
y=(2+Cosx)^x
lny=xln(2+Cosx)
y’=dy/dx
=d(2+Cosx)^x/dx
=[d(2+Cosx)^x/dln(2+Cosx)^x]*[dln(2+Cosx)^x/dx]
=(dy/dlny)*[dxln(2+Cosx)/dx]
=1/(dlny/dy)*[xdxln(2+Cosx)/dx+ln(2+Cosx)]
=1/(1/y)*[xdln(2+Cosx)/d(2+Cosx)*d(2+Cosx)/dx+ln(2+Cosx)]
=y*[x/(2+cosx)*(－Sinx)+ln(2+Cosx)]
=(2+Cosx)^x*[x/(2+Cosx)*(－Sinx)+ln(2+Ccosx)]
(E)

y = (2+Cosx)^x
lny = x ln(2+cosx)
y'/y = ln(2+cosx) + x(-sinx)/(2+cosx)
y' = y * [ln(2+cosx) + x(-sinx)/(2+cosx)]
y' = (2+cosx)^x * [ln(2+cosx) + x(-sinx)/(2+cosx)]

Answer (E)