Question

求y=／√1－x²的二阶导数

Answer 1

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

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

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

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

y''=-(1-x^2)^(-1/2)-x*(-1/2)*(1-x^2)^(-3/2)*(-2x)

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

=-(1-x^2)^(-3/2).