Answer
$f''(x) = 4xcos(x)-(x^2-2)sin(x)$
Work Step by Step
a) Using WolframAlpha and inputting "limit ((x+h)^2 * sin(x+h)-(x^2+sin(x)))/h as h approaches 0", we get $f'(x) = x(2sin(x)+xcos(x))$.
b) $f'(x) = 2x(sin(x)) + cos(x)*x^2 = x(2sin(x)+xcos(x))$
c) Using WolframAlpha and inputting "derivative of x(2sin(x)+xcos(x))", we get $f''(x) = 4xcos(x)-(x^2-2)sin(x)$