设函数f(x)在R上处处可导,已知y=f(sinx)在x=π/3处的导数为1,则f'((根号3)/2)=?

问题描述:

设函数f(x)在R上处处可导,已知y=f(sinx)在x=π/3处的导数为1,则f'((根号3)/2)=?

y=f(sinx)
y'=f'(sinx)* cosx
f'(π/3)=f'(sinπ/3)*cosπ/3=f'(√3/2)*1/2=1
得:f'(√3/2)=2