# How do you differentiate #arctan(x^2)#?

The derivative of the arctangent function is:

So, when applying the chain rule, this becomes

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Therefore

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To differentiate arctan(x^2), you can use the chain rule. Let u = x^2, then differentiate u with respect to x, du/dx = 2x. Now differentiate arctan(u) with respect to u, d(arctan(u))/du = 1/(1+u^2). By the chain rule, the derivative of arctan(u) with respect to x is the product of these two derivatives: (1/(1+u^2)) * (2x). Substituting u = x^2 back in, the derivative is 2x/(1 + x^4).

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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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