find the derivitive of f(x) e^(x^2 + 3x + 4)

[tinad]

find the derivitive of f(x) = e^x^2 teh x^2 has a +3x + 4 next to it. The e is by itself and then raised to all of that.
. . . .x^2+3x+4
. . . . . . . . e
like that.
would i pull the 2 to the front so
. . . .x + 3x + 4
. . .2e
would f ' (x) = (2x+3)e^x

 

[soroban]

Re: find the derivitive

Hello, tinad!

find the derivitive of f(x) = e^x^2 teh x^2 has a +3x + 4 next to it.
The e is by itself and then raised to all of that.

You could have said: e^(x^2 + 3x + 4)

would i pull the 2 to the front so: 2e^{x + 3x + 4} \(\displaystyle \;\) . . . no!

Use the usual Chain Rule.

\(\displaystyle \;\;\)We have: \(\displaystyle \,f(x)\;=\;e^{(x^{^2}+3x+4)}\)

\(\displaystyle \;\;\)Then: \(\displaystyle \,f'(x)\:=\:e^{(x^{^2}+3x+4)}\cdot(2x\,+\,3)\)