Question

How do you differentiate `(5-x^-1)^(1/3)`?

Answer 1

You can use the Chain Rule.
You differentiate first the the `1/3` power (leaving the argument as it is) and then multiply times the argument differentiated:

`1/3(5-x^-1)^(1/3-1)*x^-2=`

`1/3(5-x^-1)^(-2/3)*x^-2=`

`=1/3*1/(5-x^-1)^(2/3)*1/x^2`