Question

How do you differentiate `f(x)=1/(sqrt(x-3)` using the chain rule?

Answer 1

Chain rule states that `(dy)/(dx)=(dy)/(du)(du)/(dx)`.
We'll also need two power rules here.

Explanation:

• `a^-n=1/a^n`

• `a^(m/n)=root(n)(a^m)`

So, we can rewrite it as `f(x)=(x-3)^(-1/2)`

Renaming `u=x-3`, we get `f(x)=u^(-1/2)` and can now differentiate it.

`(dy)/(dx)=-1/2u^(-3/2)(1)=-1/(2(u^(3/2)))=-1/(2sqrt((x-3)^3))`