Differentiation

1. If y = Ax^k, where A and k are non-zero constants, find the value(s) of k
so that x^2(d^2 y / dx^2) +2x(dy/dx) -2y = 0

2. If y = x^2[sin(1/x)], find d^2y / dx^2.

3a. If u=f(x) and v=g(x) are functions having the second derivatives u^n
& v^n,
show that (uv)^n = vu^n +2u'v' + uv^n.
b.Hence, find the second derivative of y = x^2 (sin x)