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

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Answer 1 · 2014-07-31T01:00:10

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 .