stumped on a seemingly simple math problem..

[cdcaveman]

i figure this relates so much to options .. some of you must know this..

find the dervative.. of

3/(2x)

i thought you bring factor so you don't have fractions, put everything to a power.. like sqrt(x) is x^1/2 i'm very good at much more complex questions relative to this..
a simple one is differentiate f(x) = x(x^2+3)
=x^3+3x
f'(x) =3x^2+3
thats simple..

so question is.. how to find the derivative of 3/(2x) i'm using parenthesis here so you don't think its three halfs of x .. its three over two times x..

 

[hft_boy]

Quote from cdcaveman:

find the dervative.. of

3/(2x)

It's like (3/2) * x^-1. Use the power rule and you get -1 * (3/2) * x^-2.

 

[addchild]

Quote from cdcaveman:

i figure this relates so much to options .. some of you must know this..

find the dervative.. of

3/(2x)

i thought you bring factor so you don't have fractions, put everything to a power.. like sqrt(x) is x^1/2 i'm very good at much more complex questions relative to this..
a simple one is differentiate f(x) = x(x^2+3)
=x^3+3x
f'(x) =3x^2+3
thats simple..

so question is.. how to find the derivative of 3/(2x) i'm using parenthesis here so you don't think its three halfs of x .. its three over two times x..

dx/dy for a quotient = ((derivitive of the numerator)(denominator)-(numerator)(derivitive of the denominator))/ (denominator)^2

 

[cdcaveman]

Quote from hft_boy:

It's like (3/2) * x^-1. Use the power rule and you get -1 * (3/2) * x^-2.

because 3/(2x) = 3/2 *1/x

there for lifting the x from the denominator you get

3/2(x^-1)

then you differentiate

-1 * (3/2) ... as the first part..
then subtract 1 from the exponent of x.. putting it at X^-2
so you end up with

-3/2x^-2


that sure seems right.. and follows what you are saying..

 

[Eyez]

Quote from cdcaveman:

because 3/(2x) = 3/2 *1/x

there for lifting the x from the denominator you get

3/2(x^-1)

then you differentiate

-1 * (3/2) ... as the first part..
then subtract 1 from the exponent of x.. putting it at X^-2
so you end up with

-3/2x^-2


that sure seems right.. and follows what you are saying..

-(3x^-2)/2 or -3/(2x^2)

 

[cdcaveman]

Quote from Eyez:

-(3x^-2)/2 or -3/(2x^2)

parenthesis to be explicit..

i got negative three halfs X to the negative second..

-3/2(x)^-2

 

[Eyez]

Quote from cdcaveman:

parenthesis to be explicit..

i got negative three halfs X to the negative second..

-3/2(x)^-2

you put x^-2 in denominator, which would switch it to numerator...


3/(2x) = (3/2) * x^-1
= -1x^-2 * (3/2)

-(3x^-2)/2 or -3/(2x^2)



http://www.wolframalpha.com/widgets/view.jsp?id=c44e503833b64e9f27197a484f4257c0

 

[cdcaveman]

Quote from Eyez:

you put x^-2 in denominator, which would switch it to numerator...


3/(2x) = (3/2) * x^-1
= -1x^-2 * (3/2)

-(3x^-2)/2 or -3/(2x^2)



http://www.wolframalpha.com/widgets/view.jsp?id=c44e503833b64e9f27197a484f4257c0

now.. (3/2)*((x^-2)/1) is the same as (3/2)*(1/(x^2))

yes moving the exponent up makes it negative and the reverse respectively..
such that negative three over 2x^2 is the same thing as 3/2( x ^-2)

 

[Eyez]

Quote from cdcaveman:

now.. (3/2)*((x^-2)/1) is the same as (3/2)*(1/(x^2))

yes moving the exponent up makes it negative and the reverse respectively..
such that negative three over 2x^2 is the same thing as 3/2( x ^-2)

I guess im being a syntax nazi lol...

 

[cdcaveman]

Quote from Eyez:

I guess im being a syntax nazi lol...

at least we aren't actually arguing about the answer being right haha