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

Find domain.

Find first and second derivative

Can some one please take me through this?

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- Oct 22nd 2009, 05:50 PMel123[SOLVED] Help with domain
$\displaystyle f(x)=e^{-x^2}$

Find domain.

Find first and second derivative

Can some one please take me through this? - Oct 22nd 2009, 06:09 PMskeeter
- Oct 22nd 2009, 06:14 PMpickslides
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. - Oct 22nd 2009, 06:58 PMux0
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...

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