Chain Rule Help :/

[kss]

So I missed my first day of class and we get a take home quiz over what I missed (The Chain Rule).

I have a few problems I need help understanding.

1. y = (-3x^2+2x)^2

y' = 2(-3x^2+2x)(-6x+2)

This is what I have so far. I understand you move the power out in front and the derivative at the end. What do I do next? Multiply 2 and (-6x+2)?

y' = (-12x+24)(-3x^2+2x)

Then FOIL? or just leave it as is?

2. y = (4x^2/3-x)^3

y' = 3 (4x^2/3-x)^2 (24x-4x^2/(3-x)^2)

Im stuck at the same spot on this one as well. I brought the power out in front and used the quotient rule to find the derivative and put it at the end. I'm just not sure what to do next or if I'm even doing it right. Looks very messy.

 

[Deleted member 4993]

So I missed my first day of class and we get a take home quiz over what I missed (The Chain Rule).

I have a few problems I need help understanding.

1. y = (-3x^2+2x)^2

y' = 2(-3x^2+2x)(-6x+2)........ You are correct so far.

This is what I have so far. I understand you move the power out in front and the derivative at the end. What do I do next? Multiply 2 and (-6x+2)?

y' = (-12x+4)(-3x^2+2x)

Then FOIL? or just leave it as is? ...... Now the next step depends on the instructions given in the class. The instructor may want you to multiply it out totally or may not!

2. y = (4x^2/3-x)^3

y' = 3 (4x^2/3-x)^2 (24x-4x^2/(3-x)^2) ............ this is incorrect.

First you need to use grouping symbols (parentheses) to indicate correct order of operations. I think your equation is:

y = [4x^2/(3-x)]^3 .................. if that is correct then

y' = 3 * [4x^2/(3-x)]^2 * [8x(3-x) + 4x^2]/(3-x)^2 .... and continue.



Im stuck at the same spot on this one as well. I brought the power out in front and used the quotient rule to find the derivative and put it at the end. I'm just not sure what to do next or if I'm even doing it right. Looks very messy.

.