What is the derivative of y = arcsin(x) with respect to x?
Answer and explanation
Correct answer: D. 1 / sqrt(1 - x^2)
- Step 1: Let y = arcsin(x), so sin(y) = x. Differentiating implicitly gives cos(y) dy/dx = 1. Step 2. dy/dx = 1 / cos(y) = 1 / sqrt(1 - sin^2 y) = 1 / sqrt(1 - x^2). Answer: 1 / sqrt(1 - x^2). Why not the others: -1/sqrt(1 - x^2) is the derivative of arccos(x); 1/(1 + x^2) is the derivative of arctan(x); 1/(1 - x^2) drops the square root.
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