求y=2x*tanx导数

题目

求y=2x*tanx导数

答案

(tanx)'
= (sinx/cox)'
= (sinx)' * (1/cosx) + sinx * (1/cosx)'
= cosx/cosx + sinx * [-(cosx)'/(cosx)^2]
= 1 + sinx*sinx/(cosx)^2
= 1 + (sinx)^2/(cosx)^2
= [(cosx)^2 + (sinx)^2]/(cosx)^2
= 1/(cosx)^2
y=2xtanx
y' = (2x)' * tanx + 2x * (tanx)'
= 2 tanx + 2x /(cosx)^2
= (2sinx*cosx + 2x)/(cosx)^2
= (sin2x + 2x)/(cosx)^2