Question

What is the derivative of `sqrt(x - 2)`?

Answer 1

`f^(')=sqrt(x-2)/(2x-4)`

Explanation:

I prefer to use a particular notation.

Let `u=x-2" "` Then `" "(du)/(dx)=1`

Let `" "y=sqrt(x-2)" "=" "sqrt(u)" "=" "u^(1/2)`

`(dy)/(du)=1/2 u^(1/2-1)-> 1/2u^(-1/2)`

But `(dy)/(dx)" "=" "(du)/(dx)xx(dy)/(du)`

`=>(dy)/(du)= 1xx1/(2sqrt(x-2))`

Multiply by 1 in the form of `1=sqrt(x-2)/sqrt(x-2)`

`=>(dy)/(du)= (sqrt(x-2))/(2(x-2))" "=" "sqrt(x-2)/(2x-4)`

Or if you prefer:

`f^(')=sqrt(x-2)/(2x-4)`