[Blindmath] Chain Rule

[M Lakhani]

The chain rule goes like this:
  if y= f(u(x))
   then y' = f'(u)*u'

So for your equation:
   y=(8x^4 - 5x^2 + 1)^4

u=(8x^4 - 5x^2 - 1)
& f= u^4

Now the chain rule means 
 f'= 4u^3
Or in full:
   f'= 4*(8x^4 - 5x^2 + 1)^3

Just work through that last bit first, because now comes u'.
So we have:
   u= 8x^4 - 5x^2 + 1
=> u'= 32x^3 - 10x

I've skipped out the working for the above since you'll probably be familiar with it- if not, then link back. :)

Ok now the chain rule says: 
   y'= f'(u) *u'

So all that's left is to multiply the above two. So your answer is:
   y'=4*(32x^3 - 10x)*{(8x^4 - 5x^2 + 1)^4}

HTH
Muzz  

Sent from my iPad 

> On 19 Oct 2014, at 00:29, Jacques Chappell via Blindmath <blindmath at nfbnet.org> wrote:
> 
> I know that this problem is to be solved using the chain rule, im looking
> through my notes and its unclear to me, could somebody please explain it. I
> would appreciate the help greatly. I know how to do it, its not clear and I
> cant remember everything as I look through my notes.
> 
> y=(8x^4-5x^2+1)^4
> 
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