How do you find the derivative of #f(x)= (x-1/x+1)^3# using the chain rule?

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Answer 1 · 2018-04-17T12:55:45

#3(1-1/x^2)(x-1/x+1)^2#

We use the chain rule, which states that,

#dy/dx=dy/(du)*(du)/dx#

Let #u=x-1/x+1,:.(du)/dx=1-1/x^2#.

Then #y=u^3,dy/(du)=3u^2#.

And so,

#dy/dx=3u^2(1-1/x^2)#

Substitute back #u=x-1/x+1# to get the final answer:

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

I'll make this neater and rearrange it into:

#=3(1-1/x^2)(x-1/x+1)^2#