,
it may be the case that this derivation is not required by your particular syllabus. However, understanding how equations are derived from first principles will give you a deeper understanding of physics. This indirectly will probably lead to a better result.
The rate of decay(activity, A) is proportional to the number of parent nuclei(N) present.

λ(lambda) is a positive constant called the decay constant. It has the unit s-1 .
The minus sign is included because N decreases as the time t in seconds (s) increases .
