Question

Help with derivatives; everyone loves those, right?

Find the derivative of the function:
f(x) = (x^3 - 6x^2 + 5)/x^2

Answer 1

So far this is what I've done: rewritten the equation to look like this: x^3 - 6x^2 +5x^-2

Answer 2

use the division rule :
y = u/v
y' = (u'v - uv')/v^2

Answer 3

And tried to find the derivative, but i feel like I'm missing something; I have this so far: f'(x) = (3x^2 - 12x -10)/x^3

Answer 4

in this case,
u = x^3 - 6x^2 + 5 ----> u'= ... ?
v = x^2 ----> v' = ... ?

Answer 5

in just an alternate way, we can avoid quotient rule...

Answer 6

Oh... just do them piece by piece...

Answer 7

or u can divided all things in numerator by x^2
so, (x^3 - 6x^2 + 5)/x^2 = x^3/x^2 - 6x^2/x^2 + 5/x^2
simplify again

Answer 8

u' = 3x^2 -12x
v' = 2x

Answer 9

yes, that's right if u want use the division rule
apply it to formula above

Answer 10

@RadEn-- After applying that formula, I got the answer: f'(x) = (3/2)x -6

Answer 11

let's check it ...
y' = (u'v - uv')/v^2
y' = [(3x^2 -12x)x^2 - (x^3-6x^2+5)(2x)]/(x^2)^2
y' = (3x^4 - 12x^3 - 2x^4 + 12x^3 - 10x)/x^4
y' = (x^4 - 10x)/x^4
y' = x^4/x^4 - 10x/x^4
y' = 1 - 10/x^3
y' = 1 - 10x^(-3)
hope i didnt mistake

Answer 12

wolfram has the answer like m ;)
http://www.wolframalpha.com/input/?i=f%28x%29+%3D+%28x^3+-+6x^2+%2B+5%29%2Fx^2