# How do you differentiate #y=3^(cotx)#?

This is an interesting problem.

There are different strategies of approaching this question, but I will take what I see simplest: use of the chain rule.

By the quotient rule:

By the chain rule:

Hopefully this helps!

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To differentiate ( y = 3^{\cot(x)} ), you can use the chain rule. The derivative is:

[ \frac{dy}{dx} = -3^{\cot(x)} \cdot \ln(3) \cdot \csc^2(x) ]

where ( \csc(x) ) represents the cosecant function.

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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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