How do you differentiate $y=(1+x^2)e^x$ ?

Question

4526 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-19T16:16:28

$f'(x)=2xe^x+e^x(1+x^2)$

$(1+x^2)e^x$

This is of the form:
$f(x)=g(x)h(x)$

Where,
$g(x)=1+x^2$ and $h(x)=e^x$

Apply the product rule to find the derivatives:
$f(x)=g(x)h(x)$

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

Let's work out the derivatives of the functions, separately:

$g(x)=1+x^2$

$g'(x)=2x$

$h(x)=e^x$

$h'(x)=e^x$

Plug in these values in $f'(x)$

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

$=2x xx e^x+(1+x^2)xxe^x$

$=2xe^x+e^x(1+x^2)$

How do you differentiate y=(1+x^2)e^x y=(1+x^2)e^x ?