## Calculus (3rd Edition)

First, differentiate the functions of F(x). Then, match it to the corresponding function of f(x). i) $cos(1-x)' = -sin(1-x) \times(1-x)'$ $= -sin(1-x)\times-1 = -sin(1-x)$ = option c ii) $-cos(x)' = -(-sin(x)) = sin(x)$ = option a iii) $(-\frac{1}{2}cos(x^2))' = -\frac{1}{2}(-sin(x^2))\times2x = xsin(x^2)$ = option b iv) $(sin(x) -xcos(x))'$ $= cos(x)-(x'cos(x) + x(cos(x)')$ $= cos(x) -(cos(x) -xsin(x)) = xsin(x)$ = option d Thus, a) ii, b)iii, c)i and d)iv