What is the second derivative of #f(x)= xe^(x^2)#?

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Answer 1 · 2018-05-23T11:59:21

#f''(x) = (4x^3+6x)e^(x^2)#

#f(x) = xe^(x^2)#

#f'(x) = x * d/dx(e^(x^2)) + d/dx x * e^(x^2)#

Apply standard differential and chain rule.

#f'(x) = x* e^(x^2)* 2x + 1 * e^(x^2)#

#= (2x^2+1)e^(x^2)#

Apply product rule.

#f''(x) = (2x^2+1) * d/dx (e^(x^2)) + d/dx (2x^2+1) * e^(x^2)#

#= (2x^2+1) * 2x* e^(x^2) + 4x*e^(x^2)#

#= (4x^3 +2x + 4x)e^(x^2)#

#= (4x^3+6x)e^(x^2)#