Question

If f(x)=x/9sqrt9+x^2 find f '(x) using derivatives

Answer 1

just to clarify is this the eq. \[f(x)=\frac{x}{9 \sqrt 9}+x^2\]

Answer 2

sorry my pc died

Answer 3

f(x)= x /(9)sqrt(9+x^2))

Answer 4

it's cool my internet does it all the time

Answer 5

ok so \(f(x)=\frac{x}{9 \sqrt (9+x^2)}\)

Answer 6

yes

Answer 7

If you simplify the equation, it becomes \[\frac{ 1 }{ 27 }x+x ^{2}\]

Answer 8

i got (1/9) [(1)(9+x^2)]-(x)92x/sqrt9+x^2)/(9+x^2)^2

Answer 9

it should say ....-(x)(2x/sqrt..

Answer 10

Just to clarify, we have x[(9√(9+x^2)] ?

Answer 11

I wrote it up top Psymon

Answer 12

x/ [(9√(9+x^2)]

Answer 13

so in order to solve this you have two main options, one you can reduce the fraction or two you can apply the quotient rule

Answer 14

I am going to assume, the quotient rule is what your teacher is looking for

Answer 15

So can you type it for me please?

Answer 16

??? f'g-fg'/g^2 ?

Answer 17

Yep yep

Answer 18

(1/9) [(1)(9+x^2)]-(x)92x/sqrt9+x^2)/(9+x^2)^2 <-- i think its right

Answer 19

Not quite

Answer 20

So in our case, what is g(x)?

Answer 21

-(x)(2x... I made a typing mistake

Answer 22

Still not quite, but what is f(x) as well?

Answer 23

that it what confuses me since the demoninator says 9sqrt9+x^2 I am assuming that g shall be (9+x^2)

Answer 24

that is where the confusion lies

Answer 25

The g(x) is the entire bottom piece of the fraction so it is \(g(x)=9 \sqrt(9+x^2)\)

Answer 26

So next can you please find g'(x) showing all of your steps?

Answer 27

ooooh (9)(1/2)(9+2x)? since the 9s dont have an x should I write that they =0?

Answer 28

Not quite. Let me show you a similar ex. \[h(x)=8\sqrt(8+x^3)\]\[Let~u=8+x^3~~du=3x^2\]\[Then~we~have: ~~h(x)=8\sqrt u~du\]

Answer 29

Whoops forget the du on the last part

Answer 30

(also make the last part h(u)) ok so now, can you find the derivative of h(u)?

Answer 31

it should say 8/sqrt h(u)? is that what you meant?

Answer 32

you are appliying the chin rule, right?

Answer 33

no not h(u) I changed the variable, but yes chain rule.

Answer 34

it should read \(h(u)=8\sqrt u\)

Answer 35

8/sqrtu(u^1/2)

Answer 36

ok, not quite

Answer 37

:(

Answer 38

what is the derivative of √u?

Answer 39

1/2u ^-1/2

Answer 40

right

Answer 41

so d/dx(8√u)=?

Answer 42

8(1/2)u^-1/2

Answer 43

4u^-1/2

Answer 44

yes! but one missing piece I asked for the derivative WRT x, so that means ...

Answer 45

?