product rule: find y' for y = (x^3 + 2)(1 - x)

[jself]

I am not sure how to set up my equation on here, so I apologize for that.

The section that I am working on is The Product and Quotient Rules.

The problem is:

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

I worked it out like this:

. . .(x^3 + 2)(x) + (1 - x)(3x)
. . .x^4 + 2x + 3x - 3x^2
. . .x^4 - 3x^2 + 5x

The answer is supposed to be:

. . .y' = -4x^3 + 3x^2 - 2

I have tried everything I can think of to answer this, but I am just not able to get the correct answer.

Thanks,
jself

 

[skeeter]

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

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

y' = -x^3 - 2 + 3x^2 - 3x^3

combine like terms and you're done

 

[jself]

Thank you. That makes complete sense.