Question

What is the derivative of t^3/3

Answer 1

limit of (1/3)[(t+h)^3 -t^3]/h as h--> 0
(t+h)^3 = t^3 + 3t^2h + 3th^2 + h^3
subtract t^3
3t^2h + 3 th^2 + h^3
divide by ha
3t^2 +3th +h^2
let h --> 0
3t^2
don't forget that 1/3 up on the first line
t^2
the end

Answer 2

I do not want the limit i just need the derivative so I can set it equal to 15

Answer 3

That is the derivative.
d/dt (t^3/3) = t^2

Since you asked for the derivative, I derived the derivative.

Answer 4

Well can you make it easier to understand how you got it?

Answer 5

A derivative IS a limit !

Answer 6

I mean how you got it? Your explanation is very confusing

Answer 7

In general

Look at the tangent to f(x) at x

now look at the function a little bit further, at x + some little h

if the curve is smooth, the tangent goes close to the point
[(x+h), f(x+h) ]
as the f(x) goes up or down between x and x+h

now as h gets tiny, the slope gets closer and closer to
[f(x+h)-f(x)] / [(x+h)-h]
that denominator is h of course
so the slope (derivative) approaches
[f(x+h)-f(x)] / h as h gets tiny (goes to zero)

That is the definition of the derivative that I used to get
d/dt (t^3) = 3 t^2
or
derivative of (1/3)t^3 = t^2

Answer 8

Look in the index of your calculus book for derivative, definition of derivative. They may explain it better or search on google for "definition of derivative" calculus

Answer 9

When I did that search, one of the first results was a " Wikipedia" article that does what I did with very nice graphs and stuff so it may be easier to understand than my trying to type it freehand.

Answer 10

This is much simpler... (t^3)/3

Write as 1/3(t^3) so that the 1/3 is multiplied rather than dividing by 3.

Using the power rule, which states that the derivative of x^n is n*x^(n-1), we get...

f'(x) = (3)(1/3)(t^2) = t^2

Answer 11

That is completely correct Michael, but Britt asked where it came from. That is why I started with the definition.