To calculate the 100th derivative, it's essential to first find the initial derivatives, such as f'(x), f''(x), and f'''(x), to identify any emerging patterns. Recognizing these patterns can help in determining the nth derivative of the function. The discussion highlights the use of the Leibniz rule, which states that the nth derivative of a product of two functions can be expressed as a summation involving their derivatives. This approach allows for systematic calculation of higher-order derivatives. Understanding these techniques is crucial for effectively tackling complex derivative problems.