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Product rule help!

Given that f(x)=x(x+2)^3 find f '(x) using the product rule.

My working, I have differentiated it correctly by expanding because that was in part a and I have checked the answer with the mark scheme (4x^3+18x^2+24x+8)
I have attached a copy of my work, it's messy and my second attempt at the question! What is going wrong?!
Thank you 😄😄😄ImageUploadedByStudent Room1416157761.799915.jpg


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Reply 1
Avatar for davros
davros
16
Original post by Audi
Given that f(x)=x(x+2)^3 find f '(x) using the product rule.

My working, I have differentiated it correctly by expanding because that was in part a and I have checked the answer with the mark scheme (4x^3+18x^2+24x+8)
I have attached a copy of my work, it's messy and my second attempt at the question! What is going wrong?!
Thank you 😄😄😄ImageUploadedByStudent Room1416157761.799915.jpg


Posted from TSR Mobile


You have an extra x in your dv/dx. The derivative of (x+2)^3 is 3(x+2)^2.
Original post by Audi
Given that f(x)=x(x+2)^3 find f '(x) using the product rule.

My working, I have differentiated it correctly by expanding because that was in part a and I have checked the answer with the mark scheme (4x^3+18x^2+24x+8)
I have attached a copy of my work, it's messy and my second attempt at the question! What is going wrong?!
Thank you ImageUploadedByStudent Room1416157761.799915.jpg


Posted from TSR Mobile


I'm a bit confused by your working, did you write dv/dx as 3x(x+2)^2? Because that's wrong.
Reply 3
Avatar for 1219269
1219269
OP
3
Original post by davros
You have an extra x in your dv/dx. The derivative of (x+2)^3 is 3(x+2)^2.


Original post by Chlorophile
I'm a bit confused by your working, did you write dv/dx as 3x(x+2)^2? Because that's wrong.


I thought that you had to then times the derivative by x, as it was the derivative of the bracket?
Original post by Audi
I thought that you had to then times the derivative by x, as it was the derivative of the bracket?


Yes but the derivative of the bracket (x+2) is 1, not x!
Reply 5
Avatar for davros
davros
16
Original post by Audi
I thought that you had to then times the derivative by x, as it was the derivative of the bracket?


Yes, and what's the derivative of x with respect to x? :biggrin:
Reply 6
Avatar for 1219269
1219269
OP
3
Original post by Chlorophile
Yes but the derivative of the bracket (x+2) is 1, not x!


Original post by davros
Yes, and what's the derivative of x with respect to x? :biggrin:


hahaha indeed!!! Thank you very much! :biggrin:

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