Question

高数求导数 y=x/(x^2+1)^1/2

Answer 1

y=x(x^2+1)^(-1/2)

所以y'=1*(x^2+1)^(-1/2)+x*(-1/2)*(x^2+1)^(-1/2-1)*(x^2+1)'

=(x^2+1)^(-1/2)-x^2*(x^2+1)^(-3/2)

=1/(x^2+1)^(1/2)-x^2/[(x^2+1)(x^2+1)^(1/2)]

=(x^2+1-x^2)/[(x^2+1)(x^2+1)^(1/2)]

=1/[(x^2+1)(x^2+1)^(1/2)]