What is the derivative of y = arctan(x) with respect to x?
Answer and explanation
Correct answer: A. 1 / (1 + x^2)
- Step 1: Standard derivative formula for inverse tangent is d/dx [arctan x] = 1 / (1 + x^2). Step 2. It is positive for all real x. Answer: 1 / (1 + x^2). Why not the others: 1/(1 - x^2) uses minus sign; square root belongs to trigonometric forms; -1/(1 + x^2) is the derivative of arccot(x).
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