设f(x)可导,且f'(0=1,又y=f(x^2+sin^2x)+f(arctanx),求dy/dx /x=0
问题描述：
设f(x)可导,且f'(0=1,又y=f(x^2+sin^2x)+f(arctanx),求dy/dx /x=0
答
记g(x)=f(x^2+sin^2x)+f(arctanx)=y
g'(x)=f'(x^2+sin^2x)(2x+sin2x)+f'(arctanx)/(x2+1)
dy/dx|x=0,即g'(0)
代入得：g'(0)=1