Q:

What is the derivative of arcsin?

A:

The derivative of arcsine is equal to one divided by the square root of one minus x squared. In mathematical terms, the function is defined as d/dx arcsine(x) = 1/sqrt(1 - x^2).

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The proof to determine the derivative of arcsine of x can be written by replacing the arcsine of x with another variable, y, as in the derivative of the sine of y equals the derivative of x. Solving this equation results in the derivative of y over the derivative of x equal to one over the cosine of y. Using the Pythagorean Theorem further solves the equation by substituting for the derivative of y over the derivative of x.

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