Question

What is the derivative of `((x^2 + 1)/x)^5`?

Answer 1

`d/dx ((x^2+1)/x)^5 = (5(x^2+1)^4(x^2-1))/x^6`

Explanation:

Using the chain rule:

`d/dx ((x^2+1)/x)^5 = 5((x^2+1)/x)^4* d/dx ((x^2+1)/x)`

We can now calculate:

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

and conclude that:

`d/dx ((x^2+1)/x)^5 = 5((x^2+1)/x)^4*((x^2-1)/x^2)= (5(x^2+1)^4(x^2-1))/x^6`