(A) The given series is the expansion of the exponential function $y = e^x$. We know that $e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \ldots$. Th

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(A) The given series is the expansion of the exponential function $y = e^x$. We know that $e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \ldots$. Therefore,$y = e^x$. Differentiating both sides with respect to $x$,we get $\frac{dy}{dx} = \frac{d}{dx}(e^x) = e^x$. Since $y = e^x$,it follows that $\frac{dy}{dx} = y$. Thus,the correct option is $A$.

Class 12 Mathematics Continuity and Differentiation Derivative at a point, Standard differentiation

Easy

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

GSEB 2024 All GSEB

A
$y$
B
$y-1$
C
$0$
D
Does not exist

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Continuity and Differentiation

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Derivative at a point, Standard differentiation

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

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