Differentiating, quotient,power,chain rule

PeakingBrah

New member
Joined
Mar 10, 2014
Messages
5
Hi,

I have a homework help question. I get the rules and how to apply them, but when I apply them to the following problem I seem to get stuck. Even when looking at the solution for the problem, I can't seem to figure out where 2 of the values go.

(x2(1-x)3)/((1+x)3​)



I can see that the whole thing would have the quotient rule applied, the numerator would have the product rule and then the denominator would have the chain rule.

How would I differentiate this?

Any help is appreciated.
 
Hello. Please show us how you began. :)

Or, you could try again, after rewriting the function as

x^2 * [(1-x)/(1+x)]^3

Either way; show the beginning of your work. Cheers
 
Hello. Please show us how you began. :)

Or, you could try again, after rewriting the function as

x^2 * [(1-x)/(1+x)]^3

Either way; show the beginning of your work. Cheers

I rewrote the function like that when I originally did it, still I get stuck after the 2nd line.

I get to:

=2x((1-x)/(1+x))^3 + 3x^2((1-x)/(1+x))^2 [(-(1+x)-(1-x)(1))/(1+x)^2]

=2x((1-x)/(1+x))^3 + 3x^2((1-x)/(1+x))^2 (-2/(1+x)^2)

What happens after is what I don't get.
 
I get to:

2x((1-x)/(1+x))^3 + 3x^2((1-x)/(1+x))^2 [(-(1+x)-(1-x)(1))/(1+x)^2]

Very good. That is the correct derivative (you could omit the factor highlighted in red).

Do the instructions specifically tell you to simplify your result? If they do not, then there is nothing wrong with your answer. :cool:
 
I get the rules and how to apply them, but when I apply them to the following problem I seem to get stuck. Even when looking at the solution for the problem, I can't seem to figure out where 2 of the values go.

(x2(1-x)3)/((1+x)3​)
What were the instructions? What "rule(s)" are you supposed to be applying to this? If you're differentiating, where is the rest of the function (the "f(x)=" or whatever)? What are the "values" that are supposed to "go" somewhere?

Please provide ALL of the information for this exercise. Thank you! ;)
 
What were the instructions? What "rule(s)" are you supposed to be applying to this? If you're differentiating, where is the rest of the function (the "f(x)=" or whatever)? What are the "values" that are supposed to "go" somewhere?

Please provide ALL of the information for this exercise. Thank you! ;)
The question just states:

Differentiate y= ((x^2(1-x)^3)/(1+x)^3)

The lesson was on the chain rule.

In the solution manual, there are a few unclear steps (or what I think is unclear)solution manual diff.PNG
 
I'm not entirely sure how they went from line 2 to line 3.

\(\displaystyle \displaystyle{2x \left (\dfrac{1-x}{1+x} \right )^2}\) was factored out from each term.
 
Last edited by a moderator:
I get to:

=2x((1-x)/(1+x))^3 + 3x^2((1-x)/(1+x))^2 [(-(1+x)-(1-x)(1))/(1+x)^2]

=2x((1-x)/(1+x))^3 + 3x^2((1-x)/(1+x))^2 (-2/(1+x)^2)

The meaning of your phrase "I get to" is that you copied down some supplied answer, up to this point. Is that correct?

If not, then I'm confused.




 
Top