# How do you find the derivative of #f(x) = arctan(cos(3x))#?

Step 2. Using the chain rule again,

Step 3. Factor out constants

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To find the derivative of ( f(x) = \arctan(\cos(3x)) ), you can use the chain rule and the derivative of the arctan function. The chain rule states that if ( u ) is a function of ( x ), and ( v ) is a function of ( u ), then the derivative of their composition is given by ( \frac{dv}{dx} = \frac{dv}{du} \cdot \frac{du}{dx} ). Applying this rule:

[ \frac{d}{dx}[\arctan(\cos(3x))] = \frac{1}{1+(\cos(3x))^2} \cdot (-\sin(3x)) \cdot \frac{d}{dx}(3x) ]

[ = \frac{-3\sin(3x)}{1+(\cos(3x))^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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