Derivative of $$$\operatorname{acot}{\left(x \right)}$$$
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Your Input
Find $$$\frac{d}{dx} \left(\operatorname{acot}{\left(x \right)}\right)$$$.
Solution
The derivative of the inverse cotangent is $$$\frac{d}{dx} \left(\operatorname{acot}{\left(x \right)}\right) = - \frac{1}{x^{2} + 1}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\operatorname{acot}{\left(x \right)}\right)\right)} = {\color{red}\left(- \frac{1}{x^{2} + 1}\right)}$$Thus, $$$\frac{d}{dx} \left(\operatorname{acot}{\left(x \right)}\right) = - \frac{1}{x^{2} + 1}$$$.
Answer
$$$\frac{d}{dx} \left(\operatorname{acot}{\left(x \right)}\right) = - \frac{1}{x^{2} + 1}$$$A