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# c3 differentiation help needed - quotient rule Watch

1. quotient rule

so here's the question..
y = x^2/ (1+x)^1/2

and the answer is 4x-3x^2 / 2(1+x)^3/2

now i got the numerator but halfway through the working, the solutions said that the numerator and denominator had to be multiplied by 2(1+x)^1/2

and so resulting in with the overall denominator of 2(1+x)^3/2

can someone please explain to me why it had to be multiplied by 2(1+x)^1/2? thank you

2. You want to get rid of the on the numerator, which you can do by multiplying both the numerator and denominator by . This is because

3. Well, the quotient rule is basically

(vdu - udv)/v^2 yeah?

When you work out udv, you need to differentiate (1+x)^1/2. When you do that, you get 0.5(1+x)^-1/2. In order to get rid of that negative power, they multiply the numerator and denominator by (1+x)^1/2, so the fraction stays the same, but it becomes more simplified.

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Updated: December 27, 2010
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