Question

If y = f(u) and u = g(x),where f and g are twice differentia

Answer 1

use chain rule.

u=g(x) ==> dg/dx=du/dx=u'

y=f(u) ==> df/dx=dy/du*du/dx=dy/du*u'

d2y/dx2=d(df/dx)/dx=d(dy/du)/dx*u'+dy/du* du'/dx

=d(dy/du)/du*du/dx*u'+dy/du*d2u/dx2

=d2y/du2*du/dx*du/dx+dy/du*d2u/dx2

另外twice differentiable functions意思是“二次可导函数”