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# Indices / differentiation

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1. f(x) = (3-4√x)² / √x Show that f(x).. equals:

9x^-1/2 + Ax1/2 + B where A and B are constants to be found.

Not quite sure how t0 get that - since I got something completely different after expanding brackets etc...

9 - 12 sprtx - 12 sprtx +16x / sprt x

16x - 24sprtx +9 / sprt x

Thats not going to look like how thay want it.... but not really sure what to do and the mark scheme doesnt give much away....
2. Well, (3-4√x)² expands to 9 - 24√x +16x and if you put that all over √x you get 9x^-1/2 (1/x = -1 so 1/√x = -1/2), -24 (-24√x/√x) = -24) and +16x^1/2 (16x/√x = 16x^1/2 ---- x^1 - x^1/2 = x^1/2) so if I've differentiatied it correctly, A would be 16 and B would be -24
3. (Original post by christinajane)
f(x) = (3-4√x)² / √x Show that f(x).. equals:

9x^-1/2 + Ax1/2 + B where A and B are constants to be found.

Not quite sure how t0 get that - since I got something completely different after expanding brackets etc...

9 - 12 sprtx - 12 sprtx +16x / sprt x

16x - 24sprtx +9 / sprt x

Thats not going to look like how thay want it.... but not really sure what to do and the mark scheme doesnt give much away....

remember that

Spoiler:
Show

done
4. (Original post by DrNippleson)
Well, (3-4√x)² expands to 9 - 24√x +16x and if you put that all over √x you get 9x^-1/2 (1/x = -1 so 1/√x = -1/2), -24 (-24√x/√x) = -24) and +16x^1/2 (16x/√x = 16x^1/2 ---- x^1 - x^1/2 = x^1/2) so if I've differentiatied it correctly, A would be 16 and B would be -24

Ahh I htink I get it now - each term is divided by that sprt x - because I was just bringing the sprt x up at the very end of the equation.

This revising malarky is helping me out big time! haha forgetting little things like that!
5. (Original post by christinajane)
Ahh I htink I get it now - each term is divided by that sprt x - because I was just bringing the sprt x up at the very end of the equation.

This revising malarky is helping me out big time! haha forgetting little things like that!
I've done the same in my mocks - just got to remember that divide is minus glad I could help
6. (Original post by christinajane)
Ahh I htink I get it now - each term is divided by that sprt x - because I was just bringing the sprt x up at the very end of the equation.

This revising malarky is helping me out big time! haha forgetting little things like that!
Pretty much, all you're doing is that:

Etc... - obviously using the fact that and .

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