$\displaystyle f(x)=e^{-x^2}$
Find domain.
Find first and second derivative
Can some one please take me through this?
The function is defined for all values of x as you can square any real number and raise any real number over e.
Consider
If $\displaystyle y = e^{f(x)} \Rightarrow \frac{dy}{dx} = f'(x)e^{f(x)}$
to find the 1st.
Repeat this in conjunction with the product rule on the 1st to obtain the second.
The easiest way to understand domain is to ask yourself what values of X can i put into the function f(x)?
The derivative is just
$\displaystyle e^udu$
where your
$\displaystyle u=-X^2$
$\displaystyle
f'(x)= -2xe^{-X^2}$
and ill leave you to find the second one, in which case you will have to use the chain rule...
$\displaystyle f(x)g(x)=f'(x)g(x)+f(x)g'(x)$