Question

Derivative Problem: If you're finding the derivative of t^3 isn't it 3t^3 instead of 3t^2 because you take t^3 = t(3t^2) so when you foil it 3t^2 * t = 3t^3 but if I'm wrong can someone please explain (:

Answer 1

if you did that you would have to use the product rule
so it is 3t^2

Answer 2

are you familiar with the product rule?

Answer 3

is it 3t^2 because when you write it out it's like 1(3t^2) instead of t(3t^2)?

Answer 4

And I just learned the product rule last class, so I'm still eehhh about it.

Answer 5

well, personally I would just never pull out the t.
I would leave it as t^3
, there would be no need to pull out a t.
so (d/dt)t^3=3t^2

Answer 6

if you wanted to do the product rule of t*t^2
it would be (d/dt t)(t^2)+(t)(d/dt t^2)

Answer 7

so 1(t^2)+t(2t)

Answer 8

or t^2 +2t^2 = 3t^2
.. notice how we get the same answer.

Answer 9

are you trying to apply the product rule or the chain rule here?

Answer 10

that was just the product rule. you don't need either.

Answer 11

If it's the product rule matt already covered it
if it's the chain rule, then note that the inner function is t
and d/dt(t)=1
so it would be d/dt(t^3)=3t^2(1)=3t^2
so as matt said, neither are necessary

Answer 12

it was the product rule.