The Number that will not be changed by derivatives

The Exponential Function

1. Exponential $e=1+1+{1 \over 2!}+{1 \over 3!}+{1 \over 4!}+{1 \over 5!}+{1 \over 6!}+{1 \over 7!}....$
2. Exponential Function $e^{x}=1+x+{x^{2} \over 2!}+{x^{3} \over 3!}+{x^{4} \over 4!}+{x^{5} \over 5!}+{x^{6} \over 6!}+{x^{7} \over 7!}...$
3. Exponential Function $(e^{x})'=e^{x}$

so when every you meet Exponential just reminds yourself it will not be changed by the derivatives.

examples

ex1:$f(x)=e^{x}+x^{4}$ answer1:$f'(x)=e^{x}+4x^{3}$

ex2: $f(x)={e^{x} \over x}$ answer2: $f'(x)={(x-1)e^{x} \over x^{2}}$