What is the derivative of y=arcsin(x/3 )?

1 Answer
Jul 31, 2014

First recall the definition for derivative of arcsinx:

d/dx[arcsinx] = 1/sqrt(1-x^2).

Since we're differentiating with x/3 instead of x, we need to substitute and apply the chain rule:

d/dx[arcsin(x/3)] = d/dx[x/3] * 1/(sqrt(1-(x/3)^2))

Simplifying yields:

d/dx[arcsin(x/3)] = 1/(3sqrt(1-x^2/9)) = 1/(sqrt(9-x^2))

A page explaining this simplification in more detail can be found here .