1. The problem is to understand and explain Leibniz Theorem. 2. Leibniz Theorem is a rule used in calculus for finding the $n^{th}$ derivative of a product of two functions. 3. The formula for Leibniz Theorem is: $$\frac{d^n}{dx^n}[u(x)v(x)] = \sum_{k=0}^n \binom{n}{k} \frac{d^{n-k}}{dx^{n-k}}[u(x)] \cdot \frac{d^k}{dx^k}[v(x)]$$ 4. This means the $n^{th}$ derivative of the product $u(x)v(x)$ is the sum of all products of derivatives of $u$ and $v$ where the orders of derivatives add up to $n$. 5. Here, $\binom{n}{k}$ is the binomial coefficient, which counts the number of ways to choose $k$ derivatives from $n$. 6. To apply this theorem, you calculate derivatives of $u$ and $v$ up to order $n$, multiply them according to the formula, and sum all terms. 7. This theorem generalizes the product rule for derivatives to higher order derivatives. Final answer: Leibniz Theorem provides a formula to compute the $n^{th}$ derivative of a product of two functions as a sum involving binomial coefficients and derivatives of each function.