# What is the derivative of #f(x)=cot^-1(x)# ?

By Implicit Differentiation,

Let us look at some details.

by rewriting in terms of cotangent,

by implicitly differentiating with respect to x,

Hence,

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The derivative of ( f(x) = \cot^{-1}(x) ) is ( -\frac{1}{x^2 + 1} ).

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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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