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

  • Thread starter appplejack
  • Start date
  • #1
43
0

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.
 

Answers and Replies

  • #2
100
0

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 [itex](x-5)^3[/itex] and you should be able to get it in that form.
 
  • #3
Dick
Science Advisor
Homework Helper
26,258
618

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.
 
  • #4
Pengwuino
Gold Member
4,989
14
No expansion is necessary, simply rewrite it as [itex](x-5)(x-5)^3[/itex]. Then you'll have a term [itex]x(x-5)^3[/itex] and [itex] -5(x-5)^3[/itex].
 
  • #5
43
0
haha. Why didn't I see that? Thanks guys.
 

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