# How do you find the derivative of the function: #arctan (cos x)#?

substitute these values into (A) changing u back to x.

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To find the derivative of the function arctan(cos(x)), you apply the chain rule.

Let y = arctan(cos(x)).

Now, take the derivative of both sides with respect to x:

dy/dx = d(arctan(cos(x)))/dx.

By the chain rule, d(arctan(u))/du = 1/(1 + u^2), where u = cos(x).

So, d(arctan(cos(x)))/dx = -sin(x)/(1 + cos^2(x)).

Therefore, the derivative of arctan(cos(x)) with respect to x is -sin(x)/(1 + cos^2(x)).

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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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