What is the derivative of y = ln(x^2 + 1) with respect to x?
Answer and explanation
Correct answer: D. 2x / (x^2 + 1)
- Step 1: By chain rule, dy/dx = (1 / (x^2 + 1)) d/dx [x^2 + 1]. Step 2. d/dx [x^2 + 1] = 2x, so derivative is 2x / (x^2 + 1). Answer: 2x / (x^2 + 1). Why not the others:* 1/(x^2 + 1) omits chain rule factor 2x; 2x(x^2 + 1) multiplies instead of dividing; x/(x^2 + 1) forgets coefficient 2.
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