Am I right?!

The position of an object at time t is given by s(t) = 1 - 12t. Find the instantaneous velocity at t = 2 by finding the derivative.

I think the answer is 6.

Question

Am I right?!

The position of an object at time t is given by s(t) = 1 - 12t. Find the instantaneous velocity at t = 2 by finding the derivative.

I think the answer is 6.

sleepyhead314 · Answer

what did you get for the derivative of  1-12t ?

anonymous · Answer

I assumed it would be sqrt(12) so I got 3.46

kainui · Answer

Why would you think to assume that @TheHero ?

anonymous · Answer

Because I know when I'm looking for the derivative of 8/x x=9 for example, it would be 8/9^2

sleepyhead314 · Answer

that is true only because  the derivative of 1/x = 1/x^2

meanwhile if you have   -15x
derivative of that is just -15

power rule

kainui · Answer

Not right at all unfortunately.

Have you heard of the power rule? It basically just states that when you take a derivative you take the exponent and multiply it out front and then subtract the exponent by 1. So for instance the derivative of x^3 is 3x^2.

Similarly the derivative of 8/x is the same as 8*x^(-1) so the derivative is actually -8x^(-2) so the answer is -8/(9^2).

anonymous · Answer

Okay, so then how do we do.

The position of an object at time t is given by s(t) = 1 - 12t. Find the instantaneous velocity at t = 2 by finding the derivative.

sleepyhead314 · Answer

power rule like like   x^n =  n*x^(n-1)
so   x^1 = 1
and   -12x = -12

anonymous · Answer

Ookay...? What else..

sleepyhead314 · Answer

the derivative of any number without a variable is always 0
so   derivative of 5 is 0
derivative of -1243425  is 0
and derivative of 1 is 0

anonymous · Answer

so 12 disappears?

sleepyhead314 · Answer

the "1" part of it would disappear 

the "-12x" part turns into  -12  from the idea I described before remember?

anonymous · Answer

Right... So, then what do I after that? Do I plug in x?

kainui · Answer

$$1=x^0$$ so a constant can be written as 12x^0.

The power rule will just give you zero because the exponent is 0 when you multiply it out front.

sleepyhead314 · Answer

well tell me what you think the derivative is...

anonymous · Answer

Okay, now I'm just confused.

the derivative is -12, right?

sleepyhead314 · Answer

yes! :D

sleepyhead314 · Answer

they gave you a t=2 to trick you >,<
all you needed was the derivative :P
that'd be your answer ^_^

anonymous · Answer

Ok! Now, how do I find the velocity?

kainui · Answer

The derivative is the velocity, since velocity is the change in position.

sleepyhead314 · Answer

lol xD
velocity = derivative of position

anonymous · Answer

Oh! Alright then, thank you very much sleepyhead, have a nice day! c: