Question

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

Answer 1

It is `-1/(2sqrt((x-1)^3))`.

Explanation:

You can use the chain rule and the derivative of the power.

Your function can be written as

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

we know that the derivative of `x^n` is `nx^(n-1)`.
In this case we do not have `x^(-1/2)` but we have `(x-1)^(-1/2)`.
So we have to apply the chain rule and write

`d/dx(x-1)^(-1/2)=-1/2(x-1)^(-1/2-1)*d/dx(x-1)`

`=-1/2(x-1)^(-3/2)*1`

`=-1/(2sqrt((x-1)^3))`.