We need to find derivative of f(x) = x² e^x

Derivative of a function f(x) is given by –

f’(x) = {where h is a very small positive number}

∴ derivative of f(x) = x² e^x is given as –

f’(x) =

⇒ f’(x) =

⇒ f’(x) =

Using algebra of limits, we have –

⇒ f’(x) =

⇒

As 2 of the terms will not take indeterminate form if we put value of h = 0, so obtained their limiting value as follows –

∴ f’(x) = 0×e^{x + 0} + 2x e^{x + 0} +

Use the formula:

⇒ f’(x) = 2x e^x + x² e^x

⇒ f’(x) = 2x e^x + x² e^x

Hence,

Derivative of f(x) = x² e^x = 2x e^x + x² e^x