Question

Differentiate the function w.r.t. x from first principles.
y=(x^2+3)(x-2)/(x^2)
i spent more than ten minutes on this, i wonder if there is a simpler method to do this.

Answer 1

i took out the common factor (x-2)

Answer 2

solving for y' ??

Answer 3

yes, from first principles

Answer 4

limx->h {[f(x+h)-f(h)]/h}

Answer 5

it's lim h->0 ??

Answer 6

yes! sorry!!!! i typed that incorrectly!

Answer 7

:)

Answer 8

so is there a simpler method to do this?

Answer 9

there's never an easy way for that method....

Answer 10

the simpler method is "DERIVATIVES"

Answer 11

???

Answer 12

if it told you to use the first principle, then you have no choice but to use it. so there's no "simpler method"

Answer 13

but i have to learn to differentiate different functions from first principles

Answer 14

because it told you which method to use

Answer 15

does that make sense?

Answer 16

yes i know i have to do this by first principles, but there are still many methods to do it.. i just don't want to expand everything. should i take out the factor (x-2) or something else?

Answer 17

insane algebra skills

Answer 18

that's your only way to make it simple

Answer 19

........

Answer 20

you can also expand the numerator first then divide each term by x^2

Answer 21

only then would you use the limits

Answer 22

\[(x^2 +3)(x-2) = x^3 - 2x^2 + 3x - 6\]

\[\frac{(x^2 + 3)(x-2)}{x^2} \implies \frac{x^3 - 2x^2 + 3x - 6}{x^2} \implies x - 2 + \frac 2x - \frac 6{x^2}\]

Answer 23

i don't know if that's easier for you though

Answer 24

I think so :P, it's insane

Answer 25

ok .... thanks

Answer 26

"insane algebra skills" wasn't an exaggeration. I really was serious that that is the only way to make it simpler