Question

help differentiating. please show all steps.

Answer 1

\[\frac{ d }{ dt }(\frac{ t }{ \sqrt{1+t^2} })\]

Answer 2

Know the quotient rule?

Answer 3

\[\frac{ \sqrt{1+t^2}-t ( \frac{ t }{ \sqrt{1+t^2} }) }{ \sqrt{1+t^2}^2 }\]

Answer 4

Simplify.

Answer 5

\[=-\frac{ 1 }{ \sqrt{1+t^2}^3 }\]

Answer 6

can you show me?

Answer 7

Okay, which one are we simplifying first or second?

Answer 8

the second is the answer.

Answer 9

THus i need to change the big one into the small one... but I cannot see for the life of me how to simplify it down

Answer 10

if i distribute that t in the 2nd term in the numerator... i get t^2. i see that i can use common denominators to get the negative 1 and then divide to get the sqrt 1+t^2 to the denominator.. but what about that t^2

Answer 11

my wolfram trial expired and they wont show me anymore :)

Answer 12

I don't even use wolfram. But I feel this might be a lil long.

Answer 13

this is only a small part of the problem :)

Answer 14

@agent0smith can you help me simplify this fraction?

Answer 15

I can simplify it, like I said it could be lengthy!

Answer 16

ok please do :)

Answer 17

you can also rewrite the t(t+t^2)^-1/2

Answer 18

and use the product rule

Answer 19

trying that

Answer 20

sometimes i find that easier then quotient

Answer 21

Would still give the same thing. Either way you gotta simplify! lol

Answer 22

how do you deal with the t^2?

Answer 23

derivative is 2t, you'll have to use the chain rule.....so

Answer 24

\[\frac{ -1 }{ 2}(1+t^2)^{1/2}\]

Answer 25

all that times 2t

Answer 26

which is the derivative of the inside....the first part is the derivative of the outside

Answer 27

\[\sqrt{1+t^2}+ t(\frac{ t }{ \sqrt{1+t^2} })\]

Answer 28

like that?

Answer 29

I will distribute the negative after.

Answer 30

this thing takes forever to type out formulas.....try this
http://www.derivative-calculator.net/#expr=t%2F%28sqrt%281%2Bx%5E2%29%29&showsteps=1

Answer 31

shows it step by step of a way to solve it

Answer 32

woo very nice. thanks! definately a hard problem... and this is only 1 small part of the problem.

Answer 33

i had a typo in there, i made it in terms of x, but forgot to change the top from t to x, so change it and recalculate

Answer 34

its a helpful tool to see how to solve those