Why do we use the Chain Rule to find the derivative of the inverse sine?

#arcsinx# or #sin^-1x# is not a composite function, so why do we apply the Chain Rule to find the derivative?

1 Answer
Apr 6, 2018

Interesting question...

Explanation:

First, note here that #d/dx[sin^-1(x)]=1/(sqrt(1-x^2))#

In the derivative, the domain is #(-1,1)#.

Essentially, we limit the range of #arcsin(x)# to #(-pi/2,pi/2)#.

This way, it is a function.

(By the way, we use a capital A for arcsin to represent it as a function.)

Also, if you look at the graph of the derivative, the function "explodes" as it reaches #-1# and #1#. This is because in the graph of the original function, the wave becomes straighter and straighter vertically as we approach #1# and #-1#.