Question

f(x)=(x^2+4x+6)(4x^-2+4x^-3)
find the derivative!

Answer 1

\[y= x * z \]
\[y'= (x)' z + x (z)'\]

Answer 2

I did that part but I got confused on how to go from there.
(2x+4)(4x^-2+4x^-3)+(8x^-3-12x^-4)(x^2+4x+6)

Answer 3

what's the derivative of " 4x^{-2} "?

Answer 4

Whoops I meant to put -8x^-3

Answer 5

yes, good.
distribute.

Answer 6

I'm confused on the last part of the equation because I can't FOIL it so I'm not sure how to multiply it

Answer 7

because of negative exponents ?? you can foil it
x^2 times -8x^{-3}= -8x^{2-3} = -8x^{-1}

Answer 8

(-8x^-3-12x^-4)(x^2+4x+6) I'm not sure how to foil it if one of the parenthesis sets has 3 exponents and the other has 2?

Answer 9

we don't care about the exponents when we multiply the variables.
that's a rule for combine like terms.
2x +3x^2 isn't equal to 5x^3

Answer 10

Okay I understand that, I just don't get how to multiply it. Should I multiply x^2+4x+6 by -8x^-3 first and then by -12x^-4?

Answer 11

yes