1. Product rule

I know there are a thousand ways that people try to explain this. In Calculus for dummies it says (This * that + That * this). But this particular software package that I have called Mathtutor which is outstanding does it a bit differently.

I understand everything up until the last part.

Example: Y= ( -2t^2+1) * (3t^2-5)

Now heres the second to last step to solving the problem:

Y'= (-12 t^3+ 6t) + (-12 t^3+ 20t)

Ok folks. I understand that you have to add -12 t^3+ -12 t^3 to get 24 t^3. But what I don't understand is how you do the second part of the equation.

The answer is Y'= -24 t^3 + 26t

Sometimes from what my software is explaing the problems to me it adds up the last equation sometimes and other times it will do something like
Y'= -24 t^3 + 20 t - 6t. What I need to know is what do you descern to properly do the last part of the equation?

2. Originally Posted by 702 from 512
I know there are a thousand ways that people try to explain this. In Calculus for dummies it says (This * that + That * this). But this particular software package that I have called Mathtutor which is outstanding does it a bit differently.

I understand everything up until the last part.

Example: Y= ( -2t^2+1) * (3t^2-5)

Now heres the second to last step to solving the problem:

Y'= (-12 t^3+ 6t) + (-12 t^3+ 20t)

Ok folks. I understand that you have to add -12 t^3+ -12 t^3 to get 24 t^3. But what I don't understand is how you do the second part of the equation.

The answer is Y'= -24 t^3 + 26t

Sometimes from what my software is explaing the problems to me it adds up the last equation sometimes and other times it will do something like
Y'= -24 t^3 + 20 t - 6t. What I need to know is what do you descern to properly do the last part of the equation?
$\displaystyle Y^{\prime} = (-12t^3 + 6t) + (-12t^3 + 20t)$

Rearrange this:
$\displaystyle Y^{\prime} = (-12t^3 -12t^3) + (6t + 20t)$

$\displaystyle Y^{\prime} = -24t^3 + 26t$

-Dan

3. Originally Posted by topsquark
$\displaystyle Y^{\prime} = (-12t^3 + 6t) + (-12t^3 + 20t)$

Rearrange this:
$\displaystyle Y^{\prime} = (-12t^3 -12t^3) + (6t + 20t)$

$\displaystyle Y^{\prime} = -24t^3 + 26t$

-Dan

Y= (-3x+2) * (-2x-5)

Second to last step: Which is Y= 6x-4 + 6x + 15 = 12x + 11

Now why 12x + 11 rather then (-4 + 15) for the last equation?

Thats what I'm not understanding. Thanks for the quick response. Not trying to make things more complicated then they seem.

4. I get it.

I tend to make simple things so complex sometimes. Very simple very easy