# How do you differentiate # f(x) = cos( sin( x ))#?

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To differentiate ( f(x) = \cos(\sin(x)) ), you apply the chain rule, which states that if ( g(x) = \cos(x) ) and ( h(x) = \sin(x) ), then the derivative of ( g(h(x)) ) is ( g'(h(x)) \cdot h'(x) ).

( h'(x) = \cos(x) ) and ( g'(x) = -\sin(x) ).

So, ( f'(x) = -\sin(\sin(x)) \cdot \cos(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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