The problem involves finding the derivative of the function f(x) = e^(3x^2+x) and evaluating it at x = 2. The subject area pertains to calculus, specifically the application of the chain rule and properties of exponential functions.
The discussion is ongoing, with participants exploring different interpretations of the derivative's value. There is acknowledgment of a discrepancy between the calculated approximation and the exact expression for f'(2). Guidance has been offered regarding the simplification of ln(e).
Participants are discussing the implications of using approximations versus exact values in their calculations. There is also a note about the potential confusion arising from the use of ln(e) in the derivative expression.
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?