# Taking the derivative of a function (looks easy but I don't know how to do it)

1. Jan 17, 2012

### appplejack

1. The problem statement, all variables and given/known data
f(x) = x(x-5)^4

2. Relevant equations

3. The attempt at a solution
I used product rule and chain rule so,
1(x-5)^4 + 4x(x-5)^3(1)

The answer to this question is 5(x-5)^3(x-1). I left it like the answer above. I don't know how to expand (x-5)^4. Thanks.

2. Jan 17, 2012

Your differentiation looks right. Just factorise out the $(x-5)^3$ and you should be able to get it in that form.

3. Jan 17, 2012

### Dick

Don't expand (x-5)^4. Factor (x-5)^3 out of both terms of your answer and collect what's left.

4. Jan 17, 2012

### Pengwuino

No expansion is necessary, simply rewrite it as $(x-5)(x-5)^3$. Then you'll have a term $x(x-5)^3$ and $-5(x-5)^3$.

5. Jan 17, 2012

### appplejack

haha. Why didn't I see that? Thanks guys.