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

1 Answer
Dec 26, 2015

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)