Question

find the derivative of (-50x)/[(x^2-9)^2].

Answer 1

help please..

Answer 2

@ashii_booh show me your best guess at the derivative and I'll help you fix where you went wrong.

Anytime I come across a derivative of a quotient, I always put everything in the denominator in the numerator by changing the exponent to a negative. That way it's a simple product rule rather than a quotient rule.

Answer 3

okay let me try that..

Answer 4

\[\Large \frac{-50x}{(x^2-9)^2}\]

Use the quotient rule... if f(x) and g(x) are differentiable functions, and g(x) is not 0, then
\[\Large \frac{d}{dx}\frac{f(x)}{g(x)}= \frac{f'(x)g(x) - f(x)g'(x)}{\left[g(x)\right]^2}\]

Answer 5

@Kainui , here it is i think somethings not right. TT
(-50x)(-2x(x^2-9)(2x)+(x^2-9)^-2(-50)
-50x(-4x(x^-9))+x^4-18x^2+18(-50)
200x^4-1800x^2-50x^4+900x^2+900
150x^4-900x^2+900

Answer 6

@terenzreignz , i tried that but i think i have an incorrect answer so i need help .

Answer 7

Do you have the correct answer with you?

Answer 8

none.. thats why im here..

Answer 9

Okay, show me what you did, using the quotient rule.

Answer 10

The second term is perfect! The first one you just missed a couple things:

you wrote:
(-50x)(-2x(x^2-9)(2x)
should be:
(-50x)(-2)(x^2-9)^(-3)(2x)

So really all you messed up was the exponent from the power rule while doing the chain rule of (x^2-9)^(-2).

Answer 11

@terenzreignz , (x^2-9)^2 (-50)-(-50x(2(x^2-9)(2x))/(x^2-9)^2, then im not quite sure what next.

Answer 12

@Kainui , can i ask where -3 came from?

Answer 13

i think im confused already..

Answer 14

Yeah, so if you think of:

(x^2-9)^(-2)

and substitute (x^2-9)=u

then it becomes a little more obvious as:

u^-2

derivative is

-2u^(-3)*(du/dx)

Answer 15

Just the plain old power rule, don't stress too hard haha I'm here to help!

Answer 16

Sorry, spaced out. Kainui seems to have got this covered ^_^

Answer 17

@Kainui so it will be 200x(x^2-9)^-3 - 50x^4+900x^2-900?

Answer 18

yeah. thanks for the help, @terenzreignz

Answer 19

BTW in your quotient rule demo, the denominator should have a ^4 exponent, since it's [g(x)]^2 in the formula, but otherwise, correctly executed ^^

Answer 20

oh.yeah. i forgot.. carelessness of mine. thanks for correcting.

Answer 21

ahm.. anybody there?