# Thread: [SOLVED] Help with domain

1. ## [SOLVED] Help with domain

$f(x)=e^{-x^2}$

Find domain.
Find first and second derivative

Can some one please take me through this?

2. Originally Posted by el123
$f(x)=e^{-x^2}$

Find domain.
Find first and second derivative

Can some one please take me through this?
domain is all real numbers

$f'(x) = e^{-x^2} \cdot (-2x)$

$f''(x) = e^{-x^2} \cdot (-2) + (-2x) \cdot e^{-x^2} \cdot (-2x)$

you can clean up the algebra

3. Originally Posted by el123
$f(x)=e^{-x^2}$

Find domain.
The function is defined for all values of x as you can square any real number and raise any real number over e.

Originally Posted by el123
$f(x)=e^{-x^2}$

Find first and second derivative
Consider

If $y = e^{f(x)} \Rightarrow \frac{dy}{dx} = f'(x)e^{f(x)}$

to find the 1st.

Repeat this in conjunction with the product rule on the 1st to obtain the second.

4. Originally Posted by el123
$f(x)=e^{-x^2}$

Find domain.
Find first and second derivative

Can some one please take me through this?
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

$e^udu$

where your

$u=-X^2$

$
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...

$f(x)g(x)=f'(x)g(x)+f(x)g'(x)$