Differentiation problem (1 Viewer)

[lookoutastroboy]

Hey guys,

I'm having trouble on differentiating this expression (its easy but I cannot seem to factorise it properly - may not be doing it right anyway:

the expression is x/sqrt (x squared + 1)

If someone could show me step-by-step how to do it, it'd be greatly appreciated





Thanks in advance,
lookoutastroboy

 

[Gussy Booo]

First you have to change the surd into a power thingii lol

sqrt (x squared + 1) = (x^2+1)^1/2

Then you bring it to the numerator

x(x^2+1)^-1/2

Then you use function of a function rule to differentiate it.

(x)(2x)(-1/2) (x^2+1)^-3/2

(-x^2)^-3/2

Now you bring it back to the denominatorr and turn it back into a surd

-x^2 / Square[2]Root (x^2+1)^3

swear i have no clue what im doing,asdesgdf

 

[Timothy.Siu]

Hey guys,

I'm having trouble on differentiating this expression (its easy but I cannot seem to factorise it properly - may not be doing it right anyway:

the expression is x/sqrt (x squared + 1)

If someone could show me step-by-step how to do it, it'd be greatly appreciated





Thanks in advance,
lookoutastroboy

use quotient rule.
where u=x v=sqrt (x squared + 1)
u'=1 v'=x/sqrt(x squared+1)

so dy/dx= [sqrt(x squared + 1)-x^2/sqrt(x squared+1)]/(x squared+1)

thats pretty messy.

dy/dx=1/sqrt (x squared + 1) - x^2/(x^2+1)^(3/2)

i think

edit:dy/dx=(x^2+1)/((x^2+1)^(3/2) - x^2/(x^2+1)^(3/2)
=1 / (x^2+1)^(3/2)

thank anna

 

[annabackwards]

use quotient rule.
where u=x v=sqrt (x squared + 1)
u'=1 v'=x/sqrt(x squared+1)

so dy/dx= [sqrt(x squared + 1)-x^2/sqrt(x squared+1)]/(x squared+1)

thats pretty messy.

dy/dx=1/sqrt (x squared + 1) - x^2/(x^2+1)^(3/2)

i think

I used the quotient rule as Tim said and simplified the expression.

Click here for my solution. It's a bit blurred at the bottom but it basically says 1/(x^2 + 1)^3/2

 

[lookoutastroboy]

Thanks Timothy for the reply,

the answer is 1/(x squared + 1) to the power of 3/2



can you somehow derive that answer?




thanks again,
lookoutastroboy

 

[annabackwards]

Thanks Timothy for the reply,

the answer is 1/(x squared + 1) to the power of 3/2



can you somehow derive that answer?




thanks again,
lookoutastroboy

Baha, click the link in my above post. I guess i managed to get thre right answer after all ^^

 

[lookoutastroboy]

thanks everyone for helping me solve the problem. I guess factorisation can be a bit tricky when it involves a lot of terms

good work especially to annabackwards and timothy siu

just one small extra query if possible - does using different ways of differentiating an expression always produce the same answer?

For example, in the expression f(x) = 2x(5x-1) to the power of 1/2

PRODUCT RULE

gives answer to be

(15x-2) divided by sqrt(5x-1)

however

POWER RULE (FUNCTION OF A FUNCTION RULE)

gives answer to be

5x divided by sqrt(5x-1)

Why does this occur?

 

[addikaye03]

thanks everyone for helping me solve the problem. I guess factorisation can be a bit tricky when it involves a lot of terms

good work especially to annabackwards and timothy siu

just one small extra query if possible - does using different ways of differentiating an expression always produce the same answer?

For example, in the expression f(x) = 2x(5x-1) to the power of 1/2

PRODUCT RULE

gives answer to be

(15x-2) divided by sqrt(5x-1)

however

POWER RULE (FUNCTION OF A FUNCTION RULE)

gives answer to be

5x divided by sqrt(5x-1)

Why does this occur?

Whenever x appears twice, in seperate kinda functions you use product rule ie. xsin(x) or xe^x

Power rule is only used when it's one function raised to a power ie. (3x-1)^5

I cant really think of any other way of describing it

 

[khorne]

thanks everyone for helping me solve the problem. I guess factorisation can be a bit tricky when it involves a lot of terms

good work especially to annabackwards and timothy siu

just one small extra query if possible - does using different ways of differentiating an expression always produce the same answer?

For example, in the expression f(x) = 2x(5x-1) to the power of 1/2

PRODUCT RULE

gives answer to be

(15x-2) divided by sqrt(5x-1)

however

POWER RULE (FUNCTION OF A FUNCTION RULE)

gives answer to be

5x divided by sqrt(5x-1)

Why does this occur?

You use the product rule, because f(x) is not multiplied by a constant, but, rather, by another function (i.e g(x) = x), thus you have two functions multiplied together, and are required to use the product rule. The power rule is exactly the same as the product rule, but, because the other function is just g(x) = 1 or g(x) = 2, the derivative is always 0. which cancels that term.