Question

Find the derivative of the function.
y = x / SQRT(x^6 + 4)
y'=

Answer 1

Do you know the quotient rule?

Answer 2

yes

Answer 3

but i don't know what it means

Answer 4

So in other words the derivative of f(x) / g(x) , where f(x) is the numerator and g(x) is the denominator
is ( f'(x)g(x) - f(x)g'(x) )/ (g(x))^2

So whats f(x) and g(x) in this case?

Answer 5

f(x)=x/sqrt(x)
g(x)=x^6 + 4
?

Answer 6

there are 3, right? so which one do you do?

Answer 7

you're overthinking it,
f(x) is the numerator, which is x
and g(x) is sqrt (x^6 + 4)

Answer 8

get that so far?

Answer 9

ok

Answer 10

So we use the equation now right? so we have to find 3 things: f'(x), g'(x) and ((g(x))^2
You think you can do that?

Answer 11

why g(x)^2?

Answer 12

Isnt that part of the quotient rule?

Answer 13

oh, ok.

Answer 14

yeah so f'(x) = ? , g'(x) =? (g(x))^2 = ?

Answer 15

f'(x)= 1
g'(x)= sqrt(6x^5)
g(x)^2= x^6+4
?

Answer 16

pretty close, g'(x) = (sqrt (x^6 +4) )' right?
so lets rewrite that as (x^6 + 4) ^ (1/2), im going to use the power rule? I'm not sure what you call it but im going to bring the 1/2 to the front, subtract one to get
1/2 (x^6 + 4) ^ (-1/2) * (x^6 +4)' , but we still need to use the chain rule on the inner part so we get (1/2(x^6+4)^(-1/2) ) (6x^5)

Answer 17

thanks xNiker

Answer 18

You got how to do it?

Answer 19

i think so...

it's (1/2(x^6+4)^(-1/2) ) (6x^5)
right?

Answer 20

Thats the derivative of g(x), after you got f' , g' and g^2, you gotta sub it all back in the quotient rule

Answer 21

ok, that makes sense

Answer 22

ok, wait. now i'm tripping up over the algebra

\[\left( 1*1/2(x ^{6}+4)^{-1/2}*6x ^{5} \right)\div \left( x ^{6}+4 \right)\]

Answer 23

\[y = x/ \sqrt(x^6 + 4)\]

\[y' = ((1 * \sqrt(x^6+4)) - x * 1/2 (x^6 +4)^(-1/2) * (6x^5) ) / (x^6 +4)\]

Answer 24

how do you simplify this?

Answer 25

Does your teacher want you to simplfiy it? Idk