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Derivative of $$$\operatorname{atan}{\left(v \right)}$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dv} \left(\operatorname{atan}{\left(v \right)}\right)$$$.
Solution
The derivative of the inverse tangent is $$$\frac{d}{dv} \left(\operatorname{atan}{\left(v \right)}\right) = \frac{1}{v^{2} + 1}$$$:
$${\color{red}\left(\frac{d}{dv} \left(\operatorname{atan}{\left(v \right)}\right)\right)} = {\color{red}\left(\frac{1}{v^{2} + 1}\right)}$$Thus, $$$\frac{d}{dv} \left(\operatorname{atan}{\left(v \right)}\right) = \frac{1}{v^{2} + 1}$$$.
Answer
$$$\frac{d}{dv} \left(\operatorname{atan}{\left(v \right)}\right) = \frac{1}{v^{2} + 1}$$$A
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