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Mathematics Differentiation Help?

Stuck on this question:
Show that the gradient of y=(x^2 -1)(x-2)^3 is given by

dy/dx = (x-2)^2(5x^2 -4x-3)

Any help thanks

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Original post by Pheonix201000

Stuck on this question:
Show that the gradient of y=(x^2 -1)(x-2)^3 is given by

dy/dx = (x-2)^2(5x^2 -4x-3)

Any help thanks

You have a product... so it makes sense to use (what?) rule ?

OP

Original post by RDKGames

You have a product... so it makes sense to use (what?) rule ?

I got all that but got some nasty equation, thats looks a bit wrong for 4 marks.

Study Forum Helper

Original post by Pheonix201000

I got all that but got some nasty equation, thats looks a bit wrong for 4 marks.

What did you get?

OP

Original post by RDKGames

What did you get?

Currently:

(2x^2 -4x)^3 + (x^4 - 4x^3 + 3x^2 + 4x -4)

Found my mistake so far.

(edited 5 years ago)

Study Forum Helper

Original post by Pheonix201000

Currently:

(2x^2 -4x)^3 + (x^4 - 4x^3 + 3x^2 + 4x -4)

How did you get that??

Look, by the product rule:

\dfrac{d}{dx}[(x^2-1)(x-2)^3] = (x^2-1) \dfrac{d}{dx}(x-2)^3 + (x-2)^3 \dfrac{d}{dx}(x^2-1)

which is

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

Simplify that. You can factor out

(x-2)^2

out of there immediately.

(edited 5 years ago)

OP

Original post by RDKGames

How did you get that??

Look, by the product rule:

\dfrac{d}{dx}[(x-2)^2(5x^2-4x-3)] = (5x^2-4x-3) \dfrac{d}{dx}(x-2)^2 + (x-2)^2 \dfrac{d}{dx}(5x^2-4x-3)

which is

2(5x^2-4x-3)(x-2) + (x-2)^2(10x-4)

Simplify that. You can factor out

2(x-2)

out of there immediately.

Basically, I confused myself, and a, more confused than I started, as I have been taught this oddly I think.

I guess I'll leave it out and ask the teacher as he knows the method we do etc.

Thankds for the help

Study Forum Helper

Original post by Pheonix201000

Basically, I confused myself, and a, more confused than I started, as I have been taught this oddly I think.

I guess I'll leave it out and ask the teacher as he knows the method we do etc.

Thankds for the help

Sorry, I was looking at the wrong expression in your OP.

I have amended my post above, have a look at it again. Does it make more sense?

OP

Original post by RDKGames

Sorry, I was looking at the wrong expression in your OP.

I have amended my post above, have a look at it again. Does it make more sense?

Yep, a lot more, I took out (x-2)^2 and solved from there, not sure if that makes any difference.

Thank you

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