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

1 Answer
Mar 29, 2017

Answer:

#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#