second derivative of e^(x^3+6x^2+2x+1) (found f', but....)

[craziebbygirl]

Hi I need to find the second derivative of e^((x^3) + (6x^2) + 2x + 1)

i found f'(x) = e^((x^3) + (6x^2) + 2x + 1) * ((3x^2) + 12x +3)

but Im not sure how to go about getting f''.

Help please?

 

[mmm4444bot]

… I need to find the second derivative of e^(x^3 + 6x^2 + 2x + 1) (Note: unnecessary parentheses removed)

found f`(x) = e^(x^3 + 6x^2 + 2x + 1) * (3x^2 + 12x + 3) This is not correct (typographical error?)

but [I'm] not sure how to go about getting f" …Take the derivative of f`(x)

 

[Deleted member 4993]

Re: second derivative

Also see problem at:

viewtopic.php?f=3&t=33996

 

[BigGlenntheHeavy]

\(\displaystyle f(x) = e^{x^{3}+6x^{2}+2x+1}, Let \ u = x^{3}+6x^{2}+2x+1, \ then \ u' = 3x^{2}+12x+2, \ and \ u" = 6x+12\)

\(\displaystyle f(x) = e^{u}, \ f' (x) = u'e^{u}, \ f" (x) = u"e^{u} + (u')^{2}e^{u}\)

\(\displaystyle Hence \ f"(x) = (6x+12)e^{u} + (3x^{2}+12x+2)^{2}e^{u} = e^{x^{3}+6x^{2}+2x+1}[(6x+12)+(3x^{2}+12x+2)^{2}]\)