Derivatives?

Question

When you do a derivative like this, 3X(X^3+2X^2-9) do you do the derivative of the 3X times the rest + the derivative of the rest times 3X? or am I backwards?

Answer 1

The easiest thing to do is to distribute 3x times the quantity. So you'd have 3x^4 + 6x^3 - 27x. Then take the derivative of that.

Alternately, you can use the product rule:

First X derivative of second + second X derivative of first

If you did use product rule, the first function is 3x, and the second function is X^3+2X^2-9.

Answer 2

Yes you are right. Since you are adding, it doesn't matter which order you do it in. With something like this it may be easier to multiply the part in parentheses by 3x first so you don't even have to use the product rule. You would get:
3x^4+6x^3-27x
dy/dx=12x^3+18x^2-27

With the product rule you would have many more steps

Answer 3

If I understood what you said correctly, then yes, you're correct.
d/dx (u*v) = u*dv + v*du

So substitute
u = 3X
v = (X^3 + 2X^2 - 9)

I think you can manage the rest. Best of luck.