If `y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+ ,` show that `(dy)/(dx)=y-x^n/(n!)`

Explanation

To solve the problem, we need to differentiate the function \( y \) defined as:

\[ y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \ldots \]

This series can be recognized as the Taylor series expansion for \( e^x \), but for the purpose of this problem, we will differentiate term by term.

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