How do I take the derivative of (2x+1)^3(3-x)^2?

[silentsaber]

Homework Statement

taking the derivative of this:(2x+1)^3(3-x)^2

Answer Choices
a.) 2(2x+1)^2(3-x)(x-10)
b.) -2(2x+1)^2(3-x)(x-10)
c.) 2(2x+1)^2(3-x)(5x-3)
d.) -2(2x+1)^2(3-x)(5x-8)
e.) -12(2x+1)^2(3-x)

Homework Equations

Product rule and chain rule

The Attempt at a Solution

i was thinking of using product rule and then the chain rule

after i used the product and chain rule i get 2(3)(2x+1)^2(3-x)^2+(-1)(3-x)(2x+1)^3 ..but then when i look at the answer choices it doesn't match any am i missing a step or..?

 

[lanedance]

hey ilent saber, i'd check your working, i tink you missed a factor of 2 in the 2nd half of product rule

then look at grouping terms with (2x+1)^2(3-x), then simplifying the rest

 

[njama]

Do it this way:

$$(2x+1)^3(3-x)^2$$

$$u=2x+1, z=3-x$$

$$[(2x+1)^3(3-x)^2]'=[((2x+1)^3)'(3-x)^2+(2x+1)^3((3-x)^2)']=[(u^3)'u'(3-x)^2+(2x+1)^3((z^2)'z')]$$

Now just find the derivatives of the remaining terms.