HELP! Calculus Derivative Problem.

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HWilliams44

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I started working on a calculus derivative problem today, and got a really crazy answer as a result. I've scanned the problem with my work below. Did I do this correctly? If not, where did I go wrong? Thanks. ^.^
 

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HWilliams44 said:
I started working on a calculus derivative problem today, and got a really crazy answer as a result. I've scanned the problem with my work below. Did I do this correctly? If not, where did I go wrong? Thanks. ^.^
Click to expand...

Your second derivative is correct, but all the problem was asking for was the value of the second derivative at x = 2, which you found to be 16e^4 + 2e^2. Done!
 
HWilliams44 said:
I started working on a calculus derivative problem today, and got a really crazy answer as a result. I've scanned the problem with my work below. Did I do this correctly? If not, where did I go wrong? Thanks. ^.^
Click to expand...
There is a typo in the last line of the left side: the final e^x should be e^(x^2).

\(\displaystyle \displaystyle y''(x) = (4x^2 + 2)\ e^{x^2} \)

\(\displaystyle \displaystyle y''(2) = 18\ e^4 =\ ... \)
 
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