# How do you find the derivative of #y=ln(cos(x))# ?

Process:

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To find the derivative of ( y = \ln(\cos(x)) ), we use the chain rule. The derivative of ( \ln(u) ) with respect to ( u ) is ( \frac{1}{u} ), and the derivative of ( \cos(x) ) with respect to ( x ) is ( -\sin(x) ). So, applying the chain rule, the derivative of ( y ) with respect to ( x ) is:

[ \frac{dy}{dx} = \frac{1}{\cos(x)} \cdot (-\sin(x)) = -\frac{\sin(x)}{\cos(x)} = -\tan(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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