Question

Derivative of x^2+4/3x help

Answer 1

\(\large \frac{d}{dx} (a^n) = na^{n-1}\)

Answer 2

its a fraction

Answer 3

Coefficients don't matter that much :)

@abb0t
\[\large \color{red}* \frac{d}{dx} (a^n) = na^{n-1}\cdot \color{red}{\frac{da}{dx}}\]

Answer 4

Just sayin' @abb0t :D

Answer 5

I tried doing the quotation rule, but the answer the book gives is different than what I get

Answer 6

quotient rule?
A better way would be to treat \(\large \frac34 \) just like any constant.

Answer 7

Sometimes the solution given in a book is simplified to make the solution look "pretty" however, there are also other ways to write a solution.

Answer 8

If you have to get the derivative of
\[\Large ax\]

You wouldn't hesitate to say it's \(\large a\)


(right?)

Answer 9

\[\frac{ x ^{2}+4 }{ 3x }\]

Answer 10

thats it

Answer 11

Well, the case involving
\[\large \frac34x\]

isn't much different

Answer 12

oh okay, that clears things up :D

Answer 13

Quotient rule being
\[\Large \frac{d}{dx}\left[\frac{f(x)}{g(x)}\right]=\frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}\]

Answer 14

yes, thats what I used

Answer 15

but I get a different answer than my book

Answer 16

Okay, so it all boils down to knowing what f(x), g(x), f'(x), and g'(x) are

Answer 17

What is your answer, by the way?

Answer 18

I got \[\frac{ 3x ^{2}-12 }{ (3x)^{2} }\]

Answer 19

Okay... and what does the book say?

Answer 20

the book has this \[\frac{ (x-2)(x+2) }{ (3x)^{2} }\]

Answer 21

hehe

Answer 22

???? am I doing something wrong?

Answer 23

okay, wellI'm pretty sure it's like this...
\[\Large \frac{(x-2)(x+2)}{3x^2}\]

Answer 24

no parentheses in the denominator

Answer 25

or am I missing something?

Answer 26

yea

Answer 27

no thats what the book has

Answer 28

so what am I doing wrong

Answer 29

It's different that way. So... just keep calm and take deep breaths...
\[\Large \frac{3x^2-12}{9x^2}\]

Catch me so far?

Answer 30

yea

Answer 31

Okay, so why don't we... factor out a 3 in the numerator?
\[\Large \frac{3(x^2-4)}{9x^2}\]

Answer 32

ok, now i got it

Answer 33

>:)

Answer 34

So, everything all right now?

Answer 35

i was be stupid. yep.

Answer 36

Nah, it was the book being nitpicky :D