Question

How do you find the derivative of `arcsin(1/x)`?

Answer 1

`-1/(xsqrt(x^2-1))`

Explanation:

`d/dxarcsin(x) = 1/sqrt(1-x^2)`

For `arcsin(1/x)` use the chain rule. Differentiate inside the bracket then multiply that by the derivative for the function surrounding the bracket so:

`d/dx{1/x} = -1/x^2`

`d/dxarcsin(1/x) = -1/x^2 1/sqrt(1-(1/x)^2)`

And now simplify the denominator:

`=-1/x^2 1/sqrt((x^2-1)/x^2) = -1/x^2 x/sqrt(x^2-1) = -1/(xsqrt(x^2-1))`