Need help with exponential derivative

[andy1212]

so the chain rule to find the derivative of an exponential function says,

f'(x) = a^g(x) ln ag'(x)

I have a question saying find the derivative of when,

f(x) = e^(3x^2)+x
f'(2) = ?

I used the chain rule and came up with this,

f'(2) = e^14*13
= 15633855.69

but what I don't understand is if that's the derivative then how come the exponential function is smaller than the derivative since e^14 = 1202604.28.

Or am I doing something wrong. Thanks for your time and help!

 

[Ishuda]

For your given function
f(x) = e^g(x)
where
g(x) = 3 x² + x

Thus, as it seems you have done, we have
f'(x) = (6 x + 1) e^g(x) = (6 x + 1) f(x)
So, anytime 6x+1 is greater than 1, f'(x) will be larger than f(x).

 

[lookagain]

I have a question saying find the derivative of when,

f(x) = e^(3x^2)+x \(\displaystyle \ \ \ \)<-------
f'(2) = ?


Or am I doing something wrong. Thanks for your time and help!

andy1212, you typed that wrong. You put the close parenthesis in the incorrect place.


What you typed is equivalent to \(\displaystyle \ f(x) \ = \ e^{3x^2} \ + \ x.\)


Type "f(x) = e^(3x^2 + x)" to include everything in the exponent.