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

Apply product rule..

Apply standard differential and chain rule.

Apply product rule.

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To find the second derivative of ( f(x) = xe^{x^2} ), we first need to find the first derivative using the product rule and the chain rule. Then, we differentiate the result again using the product rule and the chain rule.

First derivative: ( f'(x) = e^{x^2} + 2x^2e^{x^2} )

Second derivative: ( f''(x) = 2xe^{x^2} + 4x^3e^{x^2} )

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