Question

If f(x) = e^ax²+bx+c the f' (x) is​

Answer 1

Given:

$f(x) = e^{ax^{2}+bx+c}$,

To Find:

If $f(x) = e^{ax^{2}+bx+c}$, find the first derivative of $f(x)$

Solution:

Given, $f(x) = e^{ax^{2}+bx+c}$

Now,  the first derivative of $f(x)$ is

$\frac{d}{dx} f(x) = e^{ax^{2}+bx+c} \frac{d}{dx}(ax^{2}+bx+c})$

$= (2ax+b)e^{ax^{2}+bx+c}$