# Taking the derivative

1. Sep 3, 2009

### silentsaber

1. The problem statement, all variables and given/known data
taking the derivative of this:(2x+1)^3(3-x)^2

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)

2. Relevant equations
Product rule and chain rule

3. 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 doesnt match any am i missing a step or..?

Last edited: Sep 3, 2009
2. Sep 3, 2009

### 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

3. Sep 4, 2009

### 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.