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

f(x) = x(x-5)^4

## 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.

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f(x) = x(x-5)^4

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

Dick
Homework Helper

f(x) = x(x-5)^4

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

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

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