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# C3 Differentiation Help watch

1. I'm stuck on the following questions:

1. y= 5x^2 - 10x + 9 / (x-1)^2

Show that dy/dx = 8 / (x-1)^2

I used the product rule to give me:

(x-1)².(10x-10) - (5x^2-10x+9).(2(x-1)) / (x-1)^4

But i can't simplify this further to give me the answer

2. Given that x=Tan 1/2y prove that dy/dx= 2/1+x²

I tried several things but i couldn't eliminate the Tan

3. f(x) = x + (3/x-1) - (12/x²+2x-3)

Show that f(x) = x²+3x+3 / x+3

I've tried getting a common denominator but i ended up with the wrong answer!

2. 1. y= 5x^2 - 10x + 9 / (x-1)^2

Show that dy/dx = 8 / (x-1)^2
This one - do you mean

If so there should be no reason to use product rule?

2. Given that x=Tan 1/2y prove that dy/dx= 2/1+x²
This one - try finding and inverting this to get

Also the identity

might come in handy...

3. f(x) = x + (3/x-1) - (12/x²+2x-3)
Useful thing to notice here is that

That might help...
3. Hey Ridium, ok lets see if I can be of some help here ;D

1. Ok for this question, notice that you have a quadratic over a quadratic

Now its would be simpler to simlify this first, this is a 'top heavy' polynomial fraction, how can you simplify this, familiar with polynomial long division, I belive you learn that in C3 . Also I dont think that the end result is correct, I think it should be:

does it actually say show the equation you quoted?

2. Ok with this one you actually no not have to eliminate tan from the equations, this is implicit differentiation, a term you hopefully have come accross before, consider this:

can you see how I have applied the chain rule here, imagine rite now that your not differentiaing one side of an equation but individual terms, whats the diriviate of x with respect to x, whats the derivative of tan 1/2y wrt y. have a think. (EDIT: spread_logic's why is much simpler than mine for a method to question 2 if you dont understand this way )

3. Ok first can you factorize x^2 + 2x -3, could (x-1) be a factor, ;D I cant say anymore on that.

Have a think about that, then have a go at trying to solve them again

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Updated: February 7, 2010
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