# How do you find the derivative of #y=e^(x^2)# ?

You could do this problem by using the chain rule. You have a function "within a function", so by the chain rule, you would derive the "outer" function first (while leaving the inner function alone) and then you would times that by the derivative of the "inner" function.

Let's derive the outer function first (while leaving the inner function alone, that is):

Deriving the inner function:

Combining the two through multiplication, the actual derivative is:

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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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