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 (:

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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 (:

Mathematics
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if you did that you would have to use the product rule so it is 3t^2
are you familiar with the product rule?
is it 3t^2 because when you write it out it's like 1(3t^2) instead of t(3t^2)?

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Other answers:

And I just learned the product rule last class, so I'm still eehhh about it.
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
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)
so 1(t^2)+t(2t)
or t^2 +2t^2 = 3t^2 .. notice how we get the same answer.
are you trying to apply the product rule or the chain rule here?
that was just the product rule. you don't need either.
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
it was the product rule.

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