Find the derivative of the function(Quotient rule)

[GustX]

Homework Statement

Find the derivative of the function

<br /> y = (3-2x^3+x^6 )/x^9<br />

Homework Equations

Derivatives

The Attempt at a Solution

I have tried to use the quotient rule

and got to
<br /> -6x^11 + 6x^14 - 27x^8 + 18x ^24 - 9x ^14 / (x^9)^2 <br />
Which doesn't look close to the answer
<br /> -27/x^10 + 12/x^7 - 3 / x^4<br />

 

[fresh_42]

Can you type in the steps to see what you have done so far? And you can as well use the product rule, it's the same.
I assume you have calculated $(-9)(-2x^3)x^{8} = 18x^{24}$ which is wrong. It has to be $18x^{11}$.

 

[GustX]

Can you type in the steps to see what you have done so far? And you can as well use the product rule, it's the same.

1st Part

(-6x^2+6x^5)(x^9) - ( 3-2x^3 + x^6) (9x^8)

2nd Part

-6x^11 + 6x^14 - (27x^8 - 18x^24 + 9x^14)

3rd Part

-6x^11+6x^14 - 27x^8 + 18x^24-9x^14

lol its hard to type math with itex
finished posting.

 

[fresh_42]

1st Part

(-6x^2+6x^5)(x^9) - ( 3-2x^3 + x^6) (9x^8)

2nd Part

-6x^11 + 6x^14 - (27x^8 - 18x^24 + 9x^14)

3rd Part

-6x^11+6x^14 - 27x^8 + 18x^24-9x^14

lol its hard to type math with itex
finished posting.

See my editorial above: $x^3 \cdot x^8 = x^{11}$ not $x^{24}$.

 

[GustX]

See my editorial above: $x^3 \cdot x^8 = x^{11}$ not $x^{24}$.

Ah I see, I changed it up and it seems closer to the answer, but how do you transform from

(-27x^8+12x^11 - 3x^14)/ ((x^9)^2)

to( what do we do to the denominator)

-27/x^10 + 12/ x^7 - 3/ x^4

which is the answer

 

[fresh_42]

$(x^9)^2 = x^{18}$ and $\frac{1}{x^{18}}=x^{-18}$. So for example the first term is $-27x^8 \cdot x^{-18}= -27x^{-10}=\frac{-27}{x^{10}}$.

 

[GustX]

$(x^9)^2 = x^{18}$ and $\frac{1}{x^{18}}=x^{-18}$. So for example the first term is $-27x^8 \cdot x^{-18}= -27x^{-10}=\frac{-27}{x^{10}}$.

lol I never woulda thought it that far