The discussion revolves around the differentiation of the function f(x) = x(x-5)^4, focusing on the application of the product rule and chain rule in calculus.
Participants have provided guidance on factoring rather than expanding the expression. There is an ongoing exploration of how to manipulate the terms to reach a desired form, with no explicit consensus on a single approach yet.
Some participants express uncertainty about the necessity of expanding (x-5)^4 and are considering different methods to simplify their results.
appplejack said: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.
appplejack said: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.