Noise's impact on biochemical systems has long been a focal point of investigation, given its potential to compromise signal accuracy and disrupt system functionality. This paper conducts a comprehensive exploration into the noise characteristics within a set of signal differentiators recognized for their high precision. Noteworthy for their modularity, swift computation, and ease of implementation, these differentiators play a pivotal role in computing concentration changes and bear the potential to regulate the dynamics of biological systems. This study establishes a comprehensive simulation framework to examine the noise characteristics of these differentiators across diverse input signal scenarios. Furthermore, we also apply noise suppression techniques such as noise filters to mitigate excessive noise and enhance noise performance. Our findings reveal that these differentiators significantly amplify the system noise level, surpassing both the Poisson level and the original system noise level. Moreover, while noise filters demonstrate notable success in noise reduction, achieving Poisson-level noise without compromising signal integrity remains a challenge. This investigation yields invaluable insights into the noise properties of biochemical differentiators, shedding light on their inherent limitations. Additionally, it presents a viable pathway to enhance noise behaviour, thereby extending the scope of applications for these differentiators.