Question

How do you find the derivative of `1/sqrt(1-x^2)`?

Answer 1

`x/(1-x^2)^(3/2)` or `x(1-x^2)^(-3/2)`

Explanation:

This can be done basically using the chain rule. This is easier to understand if you use a substitution.
let `t=(1-x^2)`
so `dt/dx = -2x`
Then `f(t) = 1/sqrt(t) = t^(-1/2)`
`(df)/dt = -1/2*t^(-3/2)`
`(df)/dx = (df)/dt*(dt)/dx`
`=-1/(2t^(3/2) )* -2x`
`=x/(1-x^2)^(3/2)` or `x(1-x^2)^(-3/2)`