Question

What is the derivative of `f(x)=(1/x+lnx)^2`?

Answer 1

We'll need chain rule, here.

Explanation:

Chain rule states that `(dy)/(dx)=(dy)/(du)(du)/(dx)` and is used when it is not possible to directly derivate the function we have.

So, renaming `u=1/x+lnx`, we get:

`(dy)/(dx)=2u*(-1/x^2+1/x)`

`(dy)/(dx)=2(1/x+lnx)(-1/x^2+1/x)`

`(dy)/(dx)=2(-1/x^3+(1-lnx)/x^2+lnx/x)`