求导dy/dx:y=(4+x^2)(arctan x/2)

问题描述:

求导dy/dx:y=(4+x^2)(arctan x/2)

y'=2x(arctan x/2)+(4+x^2)*[1/(1+x^2/4)]*1/2

y'=(4+x^2)'(arctan x/2)+(4+x^2)(arctan x/2)'
=2x(arctan x/2)+(4+x²)*[1/(1+x²/4)]*1/2
=2x(arctan x/2)+(4+x²)*2/(4+x²)
=2x(arctan x/2)+2