# How do you find the 1st and 2nd derivative of #e^(x^2)#?

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To find the first derivative of ( e^{x^2} ), use the chain rule:

[ \frac{d}{dx} e^{x^2} = 2x \cdot e^{x^2} ]

To find the second derivative, differentiate the first derivative with respect to ( x ) again:

[ \frac{d^2}{dx^2} e^{x^2} = (2 + 4x^2) \cdot e^{x^2} ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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