Calculus problem :I Will be awarded

Question

anonymous · Answer

$$\frac{ x^{4}-7x+8 }{ x ^{3}}$$

anonymous · Answer

I got to this:

amistre64 · Answer

and what did you start with?

amistre64 · Answer

.. and where is it wanting to go?

anonymous · Answer

$$\frac{ x^3(4x ^{3}-7)-(x ^{4}-7x+8)(3x^2) }{ (x^3)^2 }$$

anonymous · Answer

I'm trying to get to 1+14x^-3+24x^-4

amistre64 · Answer

i believe your making life way to difficult for yourself ... unless you HAVE to work a quotient rule.

what did you start with and what are you trying to do to it?

we cant very well say your on the right track ...

anonymous · Answer

why wouldn't I use the quotient rule?

amistre64 · Answer

its messy and a pain to keep track of

anonymous · Answer

True that^

amistre64 · Answer

$$\frac{ x^{4}-7x+8 }{ x ^{3}}=x^{-3}(x^{4}-7x+8 )\color{red}{\implies}x-7x^{-2}+8x^{-3}$$
now its just power rules .....

isaiah.feynman · Answer

Is this a derivative?

anonymous · Answer

Yes

anonymous · Answer

That looks nicer...

isaiah.feynman · Answer

Of course, smart use of algebra.

amistre64 · Answer

[x -7x^(-2) +8x^(-3)] ' = 1 +14x^(-3) -24x^(-4)

amistre64 · Answer

since a/b = ab^(-1)

the quotient rule is pretty much just a novelty

[a/b]' = a' b^(-1) - ab' b^(-2)
          = (a' b - ab') b^(-2)
          = (a' b - ab')/ b^(2)

anonymous · Answer

Oohh I see