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

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Answer 1 · 2017-03-29T17:09:43

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

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:

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

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