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

[appplejack]

Homework Statement

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

Homework Equations

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.

 

[Bread18]

Homework Statement

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

Homework Equations

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 Statement

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

Homework Equations

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]

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

 

[appplejack]

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