# P3 DifferentiationWatch

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#1
Differentiate;

a.) x(x+1)³

SO;
y=x(x+1)³ u=x, v=(x+1)³

dy/dx = V du/dx + U dv/dx
dy/dx = 1.(x+1)³ + (x)(3)(x+1)²
dy/dx = (x+1)³ + 3x(x+1)²

Where do I go from here assuming what I have done is correct.
0
14 years ago
#2
(Original post by Slice'N'Dice)
Differentiate;

a.) x(x+1)³

SO;
y=x(x+1)³ u=x, v=(x+1)³

dy/dx = V du/dx + U dv/dx
dy/dx = 1.(x+1)³ + (x)(3)(x+1)²
dy/dx = (x+1)³ + 3x(x+1)²

Where do I go from here assuming what I have done is correct.
The question asks you to differentiate it, and you have differentiated it correctly. I think you can stop there.

Galois.
0
14 years ago
#3
(Original post by Slice'N'Dice)
Differentiate;

a.) x(x+1)³

SO;
y=x(x+1)³ u=x, v=(x+1)³

dy/dx = V du/dx + U dv/dx
dy/dx = 1.(x+1)³ + (x)(3)(x+1)²
dy/dx = (x+1)³ + 3x(x+1)²

Where do I go from here assuming what I have done is correct.
dy/dx is the derivative.
So the derivative of x(x+1)^3 is (x+1)³ + 3x(x+1)², as you've done.
There's not really anywhere to go, unless you want to tidy the expression. Eg:

(x+1)^2[(x+1) + 3x] = (x+1)^2[4x+1] = (4x+1)(x+1)^2
0
#4
(Original post by Gaz031)
dy/dx is the derivative.
So the derivative of x(x+1)^3 is (x+1)³ + 3x(x+1)², as you've done.
There's not really anywhere to go, unless you want to tidy the expression. Eg:

(x+1)^2[(x+1) + 3x] = (x+1)^2[4x+1] = (4x+1)(x+1)^2
Ah yes, thats what I was after, the way to tidy up the expression. Is it best to tidy it up, or can I leave it as I have?
0
14 years ago
#5
(Original post by Slice'N'Dice)
Ah yes, thats what I was after, the way to tidy up the expression. Is it best to tidy it up, or can I leave it as I have?
It is nice to tidy the expression, if you can do it in a relatively simple way that will produce a more asthetically pleasing line without a page of manipulation in between.
As you do more and more questions and see how answers to proofs or general questions of this kind are laid out you will get to know what people doing maths regard as asthetically pleasing.
You wouldn't be penalised for not tidying in an exam though, provided the question did not ask for the answer in a certain form. Still, it's a good way to practice simple algebraic manipulation.
0
14 years ago
#6
(Original post by Newton)
He did differentiate it correctly Amir.

Newton.
0
#7
(Original post by Gaz031)
It is nice to tidy the expression, if you can do it in a relatively simple way that will produce a more asthetically pleasing line without a page of manipulation in between.
As you do more and more questions and see how answers to proofs or general questions of this kind are laid out you will get to know what people doing maths regard as asthetically pleasing.
You wouldn't be penalised for not tidying in an exam though, provided the question did not ask for the answer in a certain form. Still, it's a good way to practice simple algebraic manipulation.
Ah, alright I see what you mean.

Thanks guys.
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