Calculus Helphttp://www.clicksmilies.com/s0105/waffen/violent-smiley-011.gif (1 Viewer)

[kurt.physics]

Hello
:wave:

Here is my problem (this will be easy for yous because it preliminary maths),

I can understand f'(x), g'(x), dy/dx but one thing stubles me...

d/dx

and

dy/dt , [d^2]y / d[t^2] (from aplications of calculus to the physical world)

COULD ANYONE EXPLAIN THIS TO ME PLEASEEEEEEEEEEEE!!!!!!
How do i do it the long way and what does it mean????

Note i could be wrong on the way the ones ([d^2]y / d[t^2], dy/dt) are written, i cant remember of by heart

[(( doesnt d mean alittle ????))]
:burn::burn::burn::burn:

THANKS ALOTTTTTTTTTTTTTT

 

[watatank]

Here is my problem (this will be easy for yous because it preliminary maths),

I can understand f'(x), g'(x), dy/dx but one thing stubles me...

d/dx

and

dy/dt , [d^2]y / d[t^2] (from aplications of calculus to the physical world)

COULD ANYONE EXPLAIN THIS TO ME PLEASEEEEEEEEEEEE!!!!!!
How do i do it the long way and what does it mean????

Note i could be wrong on the way the ones ([d^2]y / d[t^2], dy/dt) are written, i cant remember of by heart

you are more likely to see things like dx/dt and [d^2]x/ d[t^2]

this is year 12 stuff, so you know, but its not too difficult. i'm not sure how to explain this im not the best at it, but i'll give it a go.

d/dx means differentiating (whatever variable they give you) with respect to x. its the same thing as f'(x), g'(x), dy/dx etc. except with dy/dx they have specified that you differentiate y with respect to x.

[d^2]x/ d[t^2] is simply the second derivative of dx/dt. you can think of it like (d/dt)(dx/dt), the dervative of a derivative (can you see how they got the notation?).

i might be giving too much away at the one time, but in applications of calculus world, you will not use x and y plane, you will use t (horizontal) and x (vertical) plane. this indicates position (x) at any time t. the derivative will be velocity of a particle at any time t, and the derivative of that will be the acceleration of the same particle at any time t.

if you see things like dy/dt and dx/dt it means that instead of having y in terms of x, you have both y and x in terms of a third parameter t. its generally used when you are indicating postion of a particle at a certain time. to find dy/dx you just use the chain rule. (dy/dt) / (dx/dt)

does this help?

 

[jb_nc]

If you can't remember the notation for d²y/dx² just remember to start the powers diagonally.

 

[Forbidden.]

1.
y = 2x

dy/dx = 2

OR

2.
d/dx(2x) = 2

2nd one saves time lol

 

[kurt.physics]

Thanks for all your help watatank and jb_nc. I fully understand..but one thing, just let me use an example to show my understanding.
Say an object was travelling and the graph that was produced of his velocity was f(t)= 5x^2, his velocity at say a point were t=2 would be 20 because f'(t)= 10x. Now if i found the second derivative f ''(x)= 10.

does f ''(t) mean the same as (d^2)x/d(y^2)

so i his acceleration would be 10 (f ''(t) = 10)?

But besides that, This is so frecken sweet, i actually understand
THANKS A MILLION FOR THAT!!!!

p.s. jb_nc, how did you get the small 2 to go above your d because it would save me alot of time writing d^2

THANKS !!!!!!!!!!!!!!!!!!!!!!!

 

[Forbidden.]

Thanks for all your help watatank and jb_nc. I fully understand..but one thing, just let me use an example to show my understanding.
Say an object was travelling and the graph that was produced of his velocity was f(t)= 5x^2, his velocity at say a point were t=2 would be 20 because f'(t)= 10x. Now if i found the second derivative f ''(x)= 10.

does f ''(t) mean the same as (d^2)x/d(y^2)

so i his acceleration would be 10 (f ''(t) = 10)?

But besides that, This is so frecken sweet, i actually understand
THANKS A MILLION FOR THAT!!!!

p.s. jb_nc, how did you get the small 2 to go above your d because it would save me alot of time writing d^2

THANKS !!!!!!!!!!!!!!!!!!!!!!!

IF
f''(x) is d²y/dx²
THEN ALSO,
f''(t) is d²y/dt²

t is the variable.
You were differentiating a function twice with respect to t

 

[mr_brightside]

p.s. jb_nc, how did you get the small 2 to go above your d because it would save me alot of time writing d^2

Type;

d[.sup]2[/sup]
(Do not type the full stop)

It will give you this

d²

So really, it's not going to help you save of time, rather make it look cooler.

 

[watatank]

p.s. jb_nc, how did you get the small 2 to go above your d because it would save me alot of time writing d^2

actually it won't save time but if you wana do that you put [sup ] [/sup ] thingos around it.

Thanks for all your help watatank and jb_nc. I fully understand..but one thing, just let me use an example to show my understanding.
Say an object was travelling and the graph that was produced of his velocity was f(t)= 5x^2, his velocity at say a point were t=2 would be 20 because f'(t)= 10x. Now if i found the second derivative f ''(x)= 10.

does f ''(t) mean the same as (d^2)x/d(y^2)

so i his acceleration would be 10 (f ''(t) = 10)?

as for that question you were asking

i think i confused you a little bit.

*you can't just say f(t)= 5x^2 because that's not a function in t. you can say f(t)= 5t^2 and you can say x = 5x^2 [where x = f(t) ] but you cant say f(t)= 5x^2.

*is that a graph of position or velocity? if its position then it would be f(t)= 5x^2. if you wanted to find velocity at t = 2, then you would sub t = 2 in f'(t) where it would be 10t and your answer is 20.

in this question, f''(t) is the same as d²x/dt²

 

[Forbidden.]

Type;

d[.sup]2[/sup]
(Do not type the full stop)

It will give you this

d²

So really, it's not going to help you save of time, rather make it look cooler.

Or m[.sub]1[/sub]
(Do not type the full stop)
for subscripts ... e.g

F = Gm₁m₂ / r²

 

[kurt.physics]

Sorry about that
f''(x) is d²y/dx²
THEN ALSO,
f''(t) is d²y/dt²
When i was typing it out i put f''(x) but then i noticed (after typing it out) that it was actually f''(t) so i changed all (or so i thought) f''(x)s' into f''(t)s' but missed that one
But i was right about f''(t) also means d²y/dt² wasnt i.
Thanks Everyone

 

[Forbidden.]

Sorry about that
f''(x) is d²y/dx²
THEN ALSO,
f''(t) is d²y/dt²
When i was typing it out i put f''(x) but then i noticed (after typing it out) that it was actually f''(t) so i changed all (or so i thought) f''(x)s' into f''(t)s' but missed that one
But i was right about f''(t) also means d²y/dt² wasnt i.
Thanks Everyone

yeah