Question

求y=2x*tanx导数

Answer 1

(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