Question

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

• A. $e^x$
• B. $\sin x$
• C. $y$
• D. $x$

Answer 1

Answer: (A)

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
$\frac{dy}{dx}=e^x$