I read somewhere people write gradient in covariant form because of their proposes. I think gradient expanded in covariant basis i , j , k so by invariance nature of vectors, component of gradient must be in contravariant form. However we know by transformation properties and chin rule we find it is a covariant vector. What is wrong with me ? My second question is : if gradient has been written in covariant form, what is the contravariant form of gradient ? Thank you.