Help with calculus multiple choice?

Question

Would appreciate answer and working out, thank you

Answer 1

Ans. A
Explanation:
y=f(x)
=>
y'=f '(x)=-1/(2x)
[the slope of a curve at
(x,y) is the -ve reciprocal
of that of its normal at the
same point].

Answer 2

The normal to the curve will be the negative inverse of the tangent to the curve

(dy/dx) * (2x) = -1
dy/dx = -1/(2x)
y = (-1/2) * ln|x| + C