If y - 1 - x1- - x22- - x33- - - find dydx

Given #160; y = 1 + x1! + x^22! + x^33! + ....... #160; y=e^x Differentiating on both sides d yd x=e^x=y ...

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Summation by Sigma Method

If y = 1 + ...

Question

If $y = 1 + \frac{x}{1!} + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + . . . . . . .$ find $\frac{d y}{d x}$

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Solution

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y = \frac{x}{1!} + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + . . .,

\frac{d y}{d x} =

y = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + . . . . + \frac{x^{n}}{n!}

\frac{d y}{d x}

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If $y = (1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + . . . \infty)$ show that $\frac{d y}{d x} = y .$

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