# How do you sketch the graph #y=sqrt(1+x^2)# using the first and second derivatives?

Use the chain rule to differentiate:

Using the product and chain rules:

The drawing of the graph should then look something like:

graph{sqrt(1+x^2) [-17.34, 18.7, -4.97, 13.05]}

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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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