Question

how do I find y' derivative for this

y=(x + (1/x)) (x-(1/x)) ?

Answer 1

ok
f'(x) = y
f'(x) = (x+ ( 1 / x)) ( x - (1 / x )
first use the predicate rule
f'(x) = (x + ( 1 / x )) ( 1- ( 1/ x^2) ) + ( 1 + 1 / x^2 ) ( x - (1/x ))
if you do not need to simply the answer above is perfect.

Answer 2

Thanks! Still kinda confusing but gonna analyze it more.

Answer 3

well he the product rule is used when you have two things to multiply
so if you have x * y for insistence
to take the derivative of it you you do this
dx * y + x * dy
so if you look again i did this

hits the derivative of 1/x is 1/x^2
x is 1