Exponential function and chain rule - find derivative

[pbonnie]

Homework Statement

If $f(x) = e^{3x^2+x}$, find f'(2)

Homework Equations

$f'(x) = a^{g(x)}ln a g'(x)$

The Attempt at a Solution

$f'(x) = (e^{3x^2+x})(ln e)(6x+1)$
$f'(2) = (e^{3(2)^2+2})(ln e)(6(2)+1)$
$= 2115812.288$

I was checking online and I'm seeing a different answer, but this is EXACTLY how my lesson is showing how to answer. Is this correct?

 

[Dick]

Homework Statement

If $f(x) = e^{3x^2+x}$, find f'(2)

Homework Equations

$f'(x) = a^{g(x)}ln a g'(x)$

The Attempt at a Solution

$f'(x) = (e^{3x^2+x})(ln e)(6x+1)$
$f'(2) = (e^{3(2)^2+2})(ln e)(6(2)+1)$
$= 2115812.288$

I was checking online and I'm seeing a different answer, but this is EXACTLY how my lesson is showing how to answer. Is this correct?

Looks to me like you are getting 13*e^(14). That's ok. But it's not equal to 2115812.288. How did you get that?

 

[pbonnie]

Oh I'm not sure how I managed that. Thank you :)

 

[Mark44]

The exact value of f'(2) is 13e¹⁴. If you use a calculator on this, the result is only an approximation.

BTW, there's no point in writing ln(e), since it is 1 (exactly).