Question

If $y=1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+....\infty$, then find the value of $\frac{dy}{dx}$.

Answer 1

$y=1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+........\infty$

$\Rightarrow y=e^x$

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