Question

find the derivative of y=(x²+5-1/x²)²
my steps:
y'=2[x²+5-x^(-2)](2x+2x)
=4x³+20x-4x^(-1)
but the answer given is 4x³+20x+20/x³-4/x^5
why am i wrong?

Answer 1

\[y=\left(\frac{x^{2}+5-1}{x^{2}}\right)^{2} \]??

Answer 2

\[x^2+5-\frac{1}{x^2}\]

Answer 3

your step was wrong.. at first

Answer 4

why?

Answer 5

he's right....

Answer 6

well one minor mistake

Answer 7

what have i done wrong?

Answer 8

it is derivative of y = (x^2 + 5 - 1)^2 * (x^-2)

Answer 9

the derivative of x^(-2) is not -2x

it's -2x^-3

Answer 10

so just change your 2x there with 2x^-3 and you're fine. redo the rest of the solution

Answer 11

so you use if y = fg y' = f'g + fg'

Answer 12

lgbasallote, i get it, thanks!

Answer 13

welcome. also...don't forget you still have a 2 outside..you have to distribute it to the equation too

Answer 14

try use chain rule to solve it

Answer 15

the eq is not a ratio..

Answer 16

damn..