Question

tanx的导数是1+tan²x还是sec²x?

Answer 1

y=tanx=sinx/cosx
y'=(sinx'*cosx-sinx*cosx')/(cosx)^2
=1/(cosx)^2=(secx)^2
=[(sinx)^2+(cosx)^2]/(cosx)^2=1+(tanx)^2