Answer
a) ii
b) iii
c) i
d) iv
Work Step by Step
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
