Answer:-
The derivative of arctan(x), or the inverse tangent function, is 1 divided by (1 plus x squared), written as d/dx [arctan(x)] = 1 / (1 + x²). This means that as x changes, the slope of the arctangent curve is always positive but decreases as x moves further from zero. This function is smooth and continuous for all real numbers, making it useful in calculus, especially in integrals and trigonometric substitutions. Understanding the derivative of arctan helps in analyzing rates of change involving angles and is commonly used in physics, engineering, and computer science problems.
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