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## Main Question or Discussion Point

what is the first derivative of f(x)=(1-x)

^{2}(1+x)^{3}?- Thread starter jhodzzz
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- #1

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what is the first derivative of f(x)=(1-x)^{2}(1+x)^{3}?

- #2

radou

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You have to apply two rules here - the rule for taking the derivative of a product of functions, and the rule for taking the derivative of a composition of functions. What is the product, and what is the composition? What are the composition and product rules?

- #3

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you see, that's the reason why I posted this thread. I'm somehow confused on what to use. Will I use the power rule or the product rule?? if i'm gonna use the power rule, i'll arrive on an answer like this: 2(1-x)*3(1+x)

is that correct??

- #4

radou

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You have to use both.

Let's say f (x) = g(x) * h(x), so g(x) = (1-x)^2 and h(x) = (1+x)^3.

First, apply the product rule, since you have a product of functions, i.e. f'(x) = g'(x)*h(x) + g(x)*h'(x).

Now you only need to apply the composition rule to sind g'(x) and h'(x).

- #5

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No, because you need to apply the product rule.

(fg)' is not f'g'!!

The rule is:

(fg)'=f'g+fg'.

Only when you apply this rule, you can take the derivative of f and g by the power rule when needed.

- #6

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alright2x...got it...now i'm enlightened..thanks a lot for the help.. :)

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