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  4. If y=1+(x/1!)+(x2/2!)+(x3/3!)....., then (dy/dx) is equal to

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Q. If $ y=1+\frac{x}{1!}+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{3}}}{3!}....., $ then $ \frac{dy}{dx} $ is equal to

J & K CETJ & K CET 2013

Solution:

Given,
$ y=1+\frac{x}{1!}+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{3}}}{3!}+....\infty ={{e}^{x}} $
On differentiation w, r. t. to x. We get
$ \frac{dy}{dx}={{e}^{x}} $