Exponential function and chain rule - find derivative

pbonnie
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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?
 
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pbonnie said:

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