求f(x)= x/tanx 的导数,然后带入π/4到导数中的x.

f'(x)=[x'*tanx-x*(tanx)']/(tanx)^2=[tanx-x*1/(cosx)^2]/(tanx)^2=[sinxcosx-x]/(sinx)^2f'(π/4)=[tanπ/4-π/4*1/(cosπ/4)^2]/(tanπ/4)^2=[1-π/4*1/(1/2)]/1=1-π/2