Find derivative

Question

y=(X+3)^cos(x) find the derivative

Answer 1

Use logarithmic differentiation.

y = (x+3)^cosx

lny = ln[(x+3)^cosx] = (cosx)ln(x+3)

y' / y = -(sinx)ln(x+3) + (cosx)(1/(x+3))

y' = y[-(sinxln(x+3) + cosx / (x+3)] = (x+3)^cosx [ -(sinx)ln(x+3) + cosx / (x+3) ]