If y = 1 + x + x^2 2! + x^3 3! + ..... , then dy dx = - Vidyadip

MCQ

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

✓
$y$
B
$y - 1$
C
$y + 1$
D
None of these

✓

Answer

Correct option: A.

$y$

a
(a) $y = 1 + x + \frac{{{x^2}}}{{2!}} + \frac{{{x^3}}}{{3!}} + ......\infty $==>$y = {e^x}$

Differentiating with respect to $x$ , we get $\frac{{dy}}{{dx}} = {e^x} = y$.

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