# How do you differentiate #f(x)=2^cotx#?

use logarithmic differentiation

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To differentiate ( f(x) = 2^{\cot(x)} ), you can use the chain rule for differentiation. The chain rule states that if ( g(x) ) is differentiable at ( x ) and ( f(x) ) is differentiable at ( g(x) ), then the composite function ( f(g(x)) ) is differentiable at ( x ) and its derivative is ( f'(g(x)) \cdot g'(x) ). Applying the chain rule to ( f(x) = 2^{\cot(x)} ):

( f'(x) = \ln(2) \cdot 2^{\cot(x)} \cdot (-\csc^2(x)) )

So, the derivative of ( f(x) = 2^{\cot(x)} ) is ( f'(x) = -\ln(2) \cdot \csc^2(x) \cdot 2^{\cot(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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