# What is the derivative of #y=(lnx)^(cosx)#?

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To find the derivative of ( y = (\ln x)^{\cos x} ), we can use the chain rule and the power rule for differentiation. The derivative is:

[ y' = \frac{d}{dx} \left( (\ln x)^{\cos x} \right) = (\cos x)(\ln x)^{\cos x - 1} \left( \frac{1}{x} \right) - (\ln x)^{\cos x} \ln(\ln x) \sin x ]

Therefore,

[ y' = (\ln x)^{\cos x - 1} \left( \frac{\cos x}{x} - (\ln x) \sin x \ln(\ln x) \right) ]

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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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